CFD Analysis and Assessment of the Stability and Control of a Supersonic

Irene Borillo Llorca

Supervisor: Arthur Rizzi

Royal Institute of Technology (KTH) Stockholm, Sweden March 2015 Abstract

Extensive research has been done on the aerodynamics of supersonic aircrafts, especially in the military and commercial airplanes’ field. Regarding supersonic business jets (SSBJs), two major problems have been addressed in past investigations: reducing the and decreasing the NOx emissions. This report focuses on a different aspect, the controls and stability of this type of aircrafts. This field has not been addressed thoroughly by the different companies and universities investigating SSBJs, as most of the existing concepts are preliminary designs that have not been developed extensively. With this report I try to put my two cents in analyzing the longitudinal stability and control surfaces of three different SSBJs designs. Acknowledgements

First of all, I would like to thank my supervisor Arthur Rizzi for all his guidance. Whenever I was stuck, he always tried helping me or putting me in contact with someone that could help me solve my problem. His comments always gave me more ideas that would eventually make me advance in my thesis. Jesper Oppelstrup, Mengmeng Zhang and Maximilian “Mio” Tomac have also been a great support, helping me when I had problems with one of the multiple programs that I had to learn how to use, for which I am very grateful. Special thanks to Evelyn Otero and Dr. Raj Nangia. Evelyn was the one who put me in contact with Arthur Rizzi, without her I would not be writing these words. Raj Nangia visited us at the KTH just in the right moment, he offered me lots of advice and comments on my thesis which allowed me to continue the process more smoothly. GoCart has been one of the main programs I have been using to complete the Thesis. Many thanks to Colin Johnson and Janet Zhen, president and product manager of Desktop Aeronautics, for giving me free access to this software, always answering my emails and offering me help with my doubts. I cannot obviously forget to mention my Swedish “family”, all the great people I met here which have made my stay in Stockholm unforgettable. They have been besides me for the good and the bad. We hung out, we traveled and we discovered together a new culture and exciting places, but they also listened to me talking about my thesis during hours and complaining because a program would not work. They know who they are and I could not have dreamt of meeting better people. Finally and most importantly, thank you to my parents and my sister. They have always supported me and they have allowed me to follow my dreams. I am who I am because of them and I will never be able to thank them enough for all they have done for me.

1 Contents

I Introduction 7

1 Justification for a 7

2 Objectives 8

3 Chosen Designs of Study 8 3.1 AS2 ...... 8 3.2 HISAC ...... 9 3.3 LM1021 ...... 9 3.4 Main Parameters ...... 10

4 Sonic Boom and Mitigation Techniques 11

5 SSBJs Design Aspects 11 5.1 Sizing ...... 11 5.2 Control Surface Sizing ...... 11 5.3 Aerodynamic Considerations ...... 12

6 Methodology 13 6.1 Programs Used ...... 13 6.1.1 CATIA V5 ...... 13 6.1.2 CEASIOM ...... 13 6.1.3 Digital DATCOM ...... 16 6.1.4 MSES ...... 16 6.1.5 Edge ...... 17 6.1.6 ANSYS ICEM CFD ...... 17 6.1.7 Tornado ...... 18 6.1.8 GoCart ...... 18 6.1.9 RAGE ...... 18 6.2 Procedure Followed ...... 18

II Work Done 20

7 CAD Models 20 7.1 Assumptions ...... 20 7.2 Determination of the Wing’s Airfoil ...... 22

8 Comparison of Airfoils using MSES 23 8.1 Objective ...... 23 8.2 Chosen Airfoils ...... 23 8.3 Procedure of Calculation ...... 23 8.4 Conclusions ...... 23

9 Finding the Mean Aerodynamic Chord 28

10 Estimation of the Center of Gravity and Moments of Inertia 29 10.1 AcBuilder’s Models ...... 29 10.2 Estimation using Weight and Building Module ...... 30

2 11 Building the Aerodynamic Database 30 11.1 Why Use GoCart Instead of Edge? ...... 32 11.2 Effects of Geometry, Mesh and Calculation Methods in GoCart’s Results ...... 33 11.2.1 Different Geometries ...... 33 11.2.2 Different Meshes ...... 36 11.2.3 Different Calculation Methods ...... 38 11.2.4 Conclusions ...... 41

12 Longitudinal Static Stability 41 12.1 Theoretical Background ...... 41 12.1.1 Neutral Point ...... 41 12.1.2 Static Margin ...... 43 12.1.3 Trimming Conditions ...... 43 12.2 Analysis of the SSBJs ...... 43 12.3 Optimizing the Elevators’ Size ...... 44 12.3.1 First Iteration ...... 45 12.3.2 Second Iteration ...... 46

13 Dynamic Stability and Aircraft Performance 48 13.1 Theoretical Background ...... 48 13.1.1 Longitudinal Dynamics ...... 49 13.1.2 Lateral dynamics ...... 50 13.1.3 Handling Qualities ...... 51 13.2 Analysis of the SSBJs ...... 53 13.2.1 AS2 ...... 53 13.2.2 LM1021 ...... 54

III Conclusions 58

14 Main Goals 58

15 Learned Notions 59

16 Experience Using GoCart 59

17 Future Work 60

Bibliography 62

Appendix: Database with "Existing" Supersonic Business Jets 64

3 List of Figures

3.1 Aerion AS2. Image obtained from Aerion’s webpage...... 9 3.2 HISAC low noise configuration. Image from final report of HISAC project...... 9 3.3 LM1021 N+2 low-boom model. Image from "Overview of Sonic Boom Reduction Efforts on the N+2 Supersonic Validations Program"...... 10 3.4 Evolution of Lockheed Martin’s N+2 project. Left to right: 1021, 1040, 1043 and 1044. Image from "Overview of Sonic Boom Reduction Efforts on the Lockheed Martin N+2 Supersonic Validations Program"...... 10 6.1 AS2 model built in CATIA ...... 13 6.2 LM1021 model built in CATIA ...... 13 6.3 CEASIOM architecture and data flow...... 14 6.4 Surface and volume example mesh created in SUMO and visualized with SCOPE. . . . . 14 6.5 AcBuilder’s user interface...... 15 6.6 User interface of the Weight and Balance module...... 15 6.7 MSES roadmap from "A User’s Guide to MSES 3.04" ...... 17 6.8 Box diagram showing the procedure followed to complete this thesis. The programs that were finally used are the ones inside the red box...... 19

7.1 CAD models built with RAGE (left) and SUMO (right). From top to bottom: AS2, HISAC and LM1021...... 21 7.2 Projection of reference profile (SUMO)...... 22 8.1 Different wing sections of the LM1021...... 24 8.2 NACA airfoils chosen for study ...... 24 8.3 Distribution of pressure around airfoil (MSES results)...... 25 8.4 Mach number distribution around airfoil (MSES results)...... 25 8.5 Boundary layer thickness on top surface of the airfoil (MSES results)...... 26 8.6 Boundary layer thickness on bottom surface of the airfoil (MSES results)...... 27 8.7 Mach number and angle of attack sweep for LM1021 airfoil and NACA 15003 (MSES results)...... 27 9.1 Method to find MAC of a tapered or ...... 29 10.1 Aircrafts built in AcBuilder. Left to right: AS2, HISAC and LM1021...... 30 11.1 Aerodynamic coefficients of AS2 for different geometries...... 34 11.2 Aerodynamic coefficients of HISAC for different geometries...... 35 11.3 Aerodynamic coefficients of LM1021 for different geometries...... 36 11.4 Meshes obtained with different number of refinements. Top (from left to right): HISAC 14, HISAC 11, HISAC 10. Bottom (from left to right): AS2 14, AS2 10...... 37 11.5 Aerodynamic coefficients obtained for the AS2 with different mesh refinement...... 37 11.6 Aerodynamic coefficients obtained for the HISAC with different mesh refinement...... 38 11.7 Aerodynamic coefficients of AS2 for different methods of calculation...... 39 11.8 Aerodynamic coefficients of HISAC for different methods of calculation...... 40 11.9 Aerodynamic coefficients of LM1021 for different methods of calculation...... 42 12.1 Static stability of an aircraft determined by the derivative of Cm with respect to α .... 43 12.2 Determining the trimming point...... 44 12.3 Aerodynamic coefficients obtained for HISAC with canard (v2) and without a canard (v1) 46 12.4 Aerodynamic coefficients obtained for LM1021 for different elevator sizing (first iteration) 47 13.1 Forces, moments, velocities and angles affected by the longitudinal motion of the aircraft. 49 13.2 Longitudinal modes represented in a Im-Re axis diagram...... 50 13.3 Forces, moments, velocities and angles affected by the lateral motion...... 50 13.4 Cooper-Harper scale...... 51 13.5 Classification of aircrafts...... 52 13.6 Classification of flight phases...... 52

4 13.7 Flying quality levels...... 52 13.8 Longitudinal dynamic behavior of the Aerion AS2: short-period mode (top) and phugoid mode (bottom)...... 53 13.9 Angle of attack (top) and elevator deflection (bottom) needed to trim the AS2...... 54 13.10Static margin of the AS2 for different flying speeds and altitudes...... 55 13.11Static margin of the LM1021 for different flying speeds and altitudes (original CG position). 55 13.12Static margin of the LM1021 for changed CG location...... 55 13.13Longitudinal dynamic behavior of the LM1021: short period mode (top) and phugoid mode (bottom)...... 56 13.14Trimming conditions for the LM1021: angle of attack (top), elevator deflection (bottom). 57

5 List of Tables

3.1 Main characteristics of the chosen designs ...... 10 5.1 Fuselage length in meters function of the type of aircraft ...... 12

8.1 Main characteristics of the chosen airfoils ...... 23 8.2 MSES results for M=0.5 and α=2o ...... 28 9.1 Mean aerodynamic chord of the SSBJs ...... 29 10.1 Weight breakdown...... 31 10.2 SSBJs’ total center of gravity for different weights...... 31 10.3 SSBJs’ moments of inertia...... 31 11.1 SDSA aero matrix structure ...... 32 11.2 SDSA control matrix structure ...... 32 11.3 Aerodynamic coefficients obtained with Edge and GoCart for M = Mcruise and α = 3deg 33 11.4 Mesh parameters ...... 38 11.5 Different calculation methods used for the Aerion AS2 model...... 39 11.6 Different calculation methods used for the HISAC model...... 41 11.7 Different calculation methods used for the LM1021 model...... 41 12.1 Neutral point and static margin for each SSBJ ...... 44 12.2 Trimming conditions when changing elevator deflection ...... 45 12.3 First iteration of AS2 elevator’s optimization ...... 45 12.4 HISAC elevator’s optimization ...... 47 12.5 LM1021 elevator’s optimization ...... 48

6 Part I

Introduction

1 Justification for a Supersonic Business Jet

The idea of a supersonic business jet (SSBJ) seems quite futuristic and unreachable for most of the population, but it is a great opportunity for those who have enough resources to afford this kind of aircraft. The business jet market is a growing sector whose costumers would be more than interested in a supersonic version. The market for SSBJs would include public company owners, private owners, fractional ownership and charter flights. In order for SSBJs to become a success in the aircraft business, the following key points need to be addressed: safety, security, reliability, comfort, productivity and performance. The major advantage of a SSBJ is its speed. Assuming a cruise Mach of 1.8 and a range of 5000 NM, a current 2 days business trip can be reduced to 12 hours, and worldwide coverage is achieved within 10 hours (with no range limitation). Point to point journeys, reduced security measures and being able to set the timetable are also other factors that allow the costumer to save time, when compared to regular existing flights. However, all that glitters is not gold. Three main technical issues avoid SSBJs to become a reality which are the airport noise, the sonic boom and the engine emissions. Many investigations are currently studying or have studied these matters trying to find ways to diminish these effects. Nonetheless, it is not only technical research what has to be done, regulations need to be modified and amplified to cover these issues effectively, especially those concerning supersonic flight overland, as it is a key point to achieve maximum time savings. Nowadays, the International Civil Aviation Organization (ICAO) regulation states that supersonic flight overland is allowed as long as no disturbance is created at the ground. On the other hand, supersonic flight is prohibited over the United States by an act of Congress. Another downfall in the market is its cost. The target unit cost for an SSBJ is around $85 million and one might think there are not enough costumers for this type of airplane. A few studies have been analyzing possible SSBJs sales. According to an internal market research done by Gulfstream, around 180 to 350 units would be sold over 10 years, without including special mission, government sales or fractional ownership needs. An independent market research estimates sales in 250-450 units costing between $50M and $100M per unit over a 10-20 year period. The typical threshold of a business jet is around 200 units, so it is realistic to assume that a supersonic version would be successful. When designing a SSBJ a few requirements have to be followed in order to make them attractive for the future buyers and avoid technical complications at the same time. The cruising Mach for market viability has to be higher than 1.3. The higher limit is marked by kinetic heating (which occurs at Mach numbers higher than 2) and the complexity of the intakes (increased complexity for Mach higher than 1.7). As for range, transatlantic capability is the minimum requirement for which at least 3500 NM of range are necessary. SSBJs would be even more appealing if they had transpacific capability (range higher than 5000 NM). However, this might imply too many technical complications, therefore, a range of approximately 4500 NM is a low risk compromise.

7 2 Objectives

The objective of this thesis is to analyze the stability of three different supersonic business jet designs and optimize the size of their control surfaces, focusing on the longitudinal behavior. Thus the main goals of this research are the following:

1. Study the longitudinal static stability of the three chosen designs 2. Optimize the size of their elevators 3. Study their longitudinal dynamic stability and flight performance

3 Chosen Designs of Study

Three different designs have been selected in order to study their stability and optimize their control surfaces. By choosing different designs, it is possible to compare the results and try to find an explanation to the differences obtained. The objects of study of this thesis are the Aerion AS2, the low boom configuration from project HISAC and the LM1021. The characteristics of these and similar aircrafts can be found in the appendix.

3.1 Aerion AS2

During many years, different research studies and companies have tried to find an efficient design for a supersonic business jet, but none of them has become a reality so far. In the present, two major projects seem to evolve forward: the one conducted by the company based in Boston, Spike , and the AS2 (figure 3.1) designed by Aerion Corporation headquartered in Reno.The most advanced in the design process is the AS2. Aerion has recently (September 2014) signed an agreement with the multinational company to start a collaboration project to further develop the AS2. This news was determining when choosing the configurations that would be studied, as the probabilities of this aircraft becoming a reality increased considerably. The AS2 is not a low-boom design; therefore it needs to make use of a phenomenon known as “Mach cut-off”, which will be explained in detail later in the paper. The materials used will be the following: carbon fiber for wings, fuselage, and engine ; the of the wing will be made of a titanium alloy to avoid erosion; and the internal fitting will consist in aluminum, steel and titanium. The most unique feature of this aircraft is the barely swept wing. It is designed so that it creates Neutral Laminar Flow, reducing friction a 50% compared to conventional swept or delta wings. It is rather thin and smooth to obtain 90% of laminar flow around the airflow, resulting in a considerable drag reduction, and its leading edge is relatively sharp. The airfoils used are modified bi-convex airfoils with the upper and lower surfaces slightly curved. To be able to achieve approach and landing speeds comparable to those of subsonic business jets, the wing will have high-lift flaps. Aerion and NASA have been working together to determine manufacturing tolerances and verifying that the amount of laminar flow is the expected one. About its performance, the AS2 will be both efficient at supersonic (Mach 1.4) and subsonic (Mach 0.95) speeds. The subsonic efficiency is necessary to allow viable routes over the US, as the Federal law

8 forbids supersonic flight. Above the rest of populated areas, the only concern is not to create a sonic boom on ground. This is achieved by flying between Mach 1.1 and 1.2 and thanks to the Mach cut-off phenomenon mentioned before. Finally, over water, the AS2 will be able to fly at 1.4 Mach.

Figure 3.1: Aerion AS2. Image obtained from Aerion’s webpage.

3.2 HISAC

The High Speed Aircraft (HISAC) program was launched in 2005 and co-funded by the European Com- mission to find a feasible design of a small that would meet certain environmental standards including sonic boom, engine emissions and noise. The project was coordinated by Dassault Aviation and included 37 partners from 13 countries. Four different configurations were developed and each one focused on a different aspect: low noise, long range, variable geometry and low boom. The reduction of noise is one of the biggest obstacles that has to be overcome for SSBJs to become a reality, therefore it was decided to focus the study on the low noise configuration (figure 3.2). Luckily, the department of Aerodynamics at KTH had done previous studies on this configuration, so the amount of information available was noteworthy. As for the design itself, the low noise configuration has a low aspect ratio, cranked arrow delta wing.

Figure 3.2: HISAC low noise configuration. Image from final report of HISAC project.

3.3 LM1021

NASAs supersonic project tries to overcome the technology barriers (environmental and concerning efficiency) for civil supersonic airliners. Three main programs were developed: N+1 Supersonic Business Class Aircraft (was not studied in detail), N+2 Small Supersonic Airliner, and N+3 Efficient Multi-Mach Aircraft. Two different concepts were studied in the N+2 program, being one of them the LM1021 (figure 3.3). The LM1021 is a low-boom model with capacity for 82-100 passengers developed by Lockheed Martin together with General Electric, Liberty Works and Standford University. Its sonic boom signature is 1/100 of the one of the Concord. This is achieved by creating a series of closely timed small shocks

9 instead than a big one. This is possible thanks to a very long fuselage that allows volume and lift to build up and decrease gradually. It is obvious that this model is not a business jet, but it was decided to scale it down as it had been developed more extensively and the information available was greater than with the N+1 designs. It is also important to note out that the LM1021 is only the first phase of Lockheed Martin’s project (figure 3.4) so it is expected to obtain some non-desirable behaviors when studying this model. The reason why it was chosen to study this first phase instead of other more developed stages was the lack of information about the geometry for these other phases.

Figure 3.3: LM1021 N+2 low-boom model. Image from "Overview of Sonic Boom Reduction Efforts on the Lockheed Martin N+2 Supersonic Validations Program".

Figure 3.4: Evolution of Lockheed Martin’s N+2 project. Left to right: 1021, 1040, 1043 and 1044. Image from "Overview of Sonic Boom Reduction Efforts on the Lockheed Martin N+2 Supersonic Validations Program".

3.4 Main Parameters

The main characteristics of the chosen designs are presented in table 3.1.

HISAC Low Noise Configuration Aerion AS2 LM1021 Low-Boom Model (Scaled Down) Capacity [PAX] 8 11 8-10 Length [m] 40.9 49 49 Wing Area [m2] 139 125 230 Wing Span [m] 19.1 21 17.7 Maximum Take-Off Weight [kg] 53300 52163 54890 Operational Empty Weight [kg] 25100 22588 24901 Cruise Mach Number [-] 1.8 1.4 1.6 Cruise Altitude [m] 15750 15500 15240

Table 3.1: Main characteristics of the chosen designs

10 4 Sonic Boom and Mitigation Techniques

The sonic boom is the audible component of a shock wave. It sounds like a loud explosion and follows the path of the aircraft as long as it flies at speeds greater than Mach 1. A way of characterizing the sonic boom level of an aircraft is the figure of merit (equation 4.1) which was described by Seebass and George in 1974. A figure of merit of less than 1 is considered acceptable. W eight FM = 3 (4.1) 2 Length Length and weight are the primary parameters affecting the boom. Therefore, a SSBJ must be as long as possible, light weighted and must have a slender configuration for low boom design. The three designs chosen for study mitigate the sonic boom in different ways. The Aerion AS2 uses a technique known as “Mach cut-off”. Not all booms reach the ground; some may be refracted at 1520 m above the ground depending on the atmospheric conditions (mainly temperature and winds). For this phenomenon to occur, the aircraft must be flying at a speed less than 1.2 Mach and an altitude higher than 10700 m. Lockheed Martin used shaped boom design processes to achieve a design with an acceptable quiet flight over land (less than 85 PLdB of sonic boom and 10-20 EPNdb of airport noise). As for the HISAC model, it was designed with the main objective of reducing the external noise.

5 SSBJs Design Aspects

Supersonic business jets have not become yet a reality, so there is no way to know which specific design aspects they should follow. Daniel P. Raymer gives some general ideas for supersonic aircrafts and business jets in his book “Aircraft Design: A Conceptual Approach”. In this chapter the three chosen designs will be analyzed following Raymer’s methods for initial sizing and configuration layout of an aircraft.

5.1 Fuselage Sizing

For some aircrafts, the fuselage size is determined by the payload it has to transport. This is not the case for SSBJs. Other considerations have to be taken into account like aerodynamic smoothness to diminish drag as well as the sonic boom, and being able to fit the huge fuel tanks, among others. Raymer offers a formula (equation 5.1) to calculate the initial size of the fuselage depending on the type of airplane. Obviously, SSBJs do not appear on the list but the most similar fuselage length is obtained using the values for the twin turboprop (table 5.1).

c Lengthfus = aW (5.1)

5.2 Control Surface Sizing

The whole purpose of this thesis is to study the control surfaces of the supersonic business jets, as it has not been studied before, but in Raymer’s book a few things are specified concerning conventional business jet configurations. Subsonic business jets normally have a tail with a horizontal stabilizer in

11 AS2 HISAC LM1021 MTOW [kg] 52163 53300 54890 a c Fuselage Length [m] Sailplane-unpowered 0.383 0.48 70.39 71.13 72.14 Sailplane-powered 0.316 0.48 58.08 58.68 59.52 Homebuilt-metal/wood 1.35 0.23 16.42 16.50 16.61 Homebuilt-composite 1.28 0.23 15.57 15.64 15.75 General aviation-single engine 1.6 0.23 19.46 19.56 19.69 General aviation-twin engine 0.366 0.42 35.06 35.38 35.82 Agricultural aircraft 1.48 0.23 18.00 18.09 18.21 Twin turboprop 0.169 0.51 43.03 43.50 44.16 Flying boat 0.439 0.4 33.84 34.13 34.54 Jet trainer 0.333 0.41 28.61 28.87 29.22 Jet fighter 0.389 0.39 26.90 27.13 27.44 Military cargo/bomber 0.104 0.5 23.75 24.01 24.37 Jet transport 0.287 0.43 30.64 30.93 31.32 SSBJ (real one) 49 40.9 49

Table 5.1: Fuselage length in meters function of the type of aircraft which the elevator is included. The hinge-line of the elevator should be perpendicular to the aircraft centerline to allow connecting the left and right side elevator surfaces with a torque tube, diminishing the elevator flutter tendencies. For a conventional business jet, the elevator chord should be 32% of the horizontal tail’s chord (ce/c = 0.32). The HISAC and LM1021 model have non-conventional elevator configurations (elevons and rudder- vators), therefore an idea about the initial sizing of the controls cannot be made. On the other hand, the Aerion’s AS2 model does have a conventional tail with elevator. In the AS2 3-views obtained from Aerion’s webpage, the elevator occupies 32% of the horizontal stabilizer’s total chord therefore it seems that is well sized. Nonetheless, the final sizing of the control surfaces is based on the dynamic analysis of control effectiveness, which is one of the goals of this project.

5.3 Aerodynamic Considerations

Friction drag is directly proportional to the total wetted area, so excess wetted area should be avoided. This can be accomplished by diminishing the fineness ratio ( Length ), but fat have a lot of W idthmax flow separation at the back which increases greatly the pressure drag. SSBJs have large fineness ratios, therefore, to counteract the high friction drag, the fuselage is as smooth as possible (avoiding longitudinal breaks in the contour) and the aft-fuselage deviation from the freestream is less than 12 degrees to prevent flow separation. Finally, when dealing with supersonic airplanes, the greatest concern is the supersonic wave drag (drag due to the formation of shock waves). The wave drag depends on the curvature (2nd derivative) of the volume distribution of the aircraft; therefore, it is directly related to the longitudinal change of the vehicle’s cross-sectional area. To reduce the drag as much as 50% the area rule is used, which consists in squeezing the fuselage at the point where the wing has its maximum cross-sectional area, softening the volume distribution shape. This squeezing or “coke-bottle” shaping of the fuselage can be clearly observed in the AS2 and is also visible in the HISAC and LM1021 models, but it is less obvious.

12 6 Methodology

6.1 Programs Used

6.1.1 CATIA V5 CATIA (Computer Aided Three-dimensional Interactive Application) is a 3D design commercial software developed by Dassault Systems. Engineers all around the world use it to design, simulate, analyze and manufacture a wide range of products in a variety of industries, including aerospace. For this particular thesis, three specific modules (part design, assembly design, and wireframe and surface design) were used to create initial 3D models of two of the aircrafts that were going to be studied (the AS2 and the LM1021, figures 6.1 and 6.2, respectively).

Figure 6.1: AS2 model built in CATIA

Figure 6.2: LM1021 model built in CATIA

6.1.2 CEASIOM CEASIOM (Computerized Environment for Aircraft Synthesis and Integrated Optimization Methods) is a tool developed within the SimSAC project (Simulating Stability and Control Characteristics for Use in Conceptual Design). Although the project started in November of 2006 and lasted three years, all CEASIOM modules keep being improved up to this date. Usually, in a traditional design process, the dynamic characteristics of the aircraft are not computed until the design is in a quite mature stage, which means that any modifications will imply high costs. CEASIOM’s main purpose is to enable a preliminary analysis of the aircraft’s flying qualities in the early conceptual design phases, reducing financial and technical risks. To be able to achieve this objective, CEASIOM combines different modules (figure 6.3), each one focusing on a specific field of the design

13 process. The following subsections will explain in detail the modules that have been used for this project (SUMO, AcBuilder, Weights and Balance, and SDSA).

Figure 6.3: CEASIOM architecture and data flow.

SUMO SUMO is a graphical tool that allows the creation of aircraft geometries in an easy and intuitive way. It also generates the airplane’s surface and volume meshes automatically (figure 6.4). This surface modeler was developed by Larosterna, a software development business started by Dr. David Eller from the Flight Dynamic Lab at KTH. It was first developed following the requests of the Swedish National Aeronautics Research Project DirSim and it has been further developed thanks to the SimSAC project sponsored by the European Union.

Figure 6.4: Surface and volume example mesh created in SUMO and visualized with SCOPE.

Two different surfaces can be used when defining the geometry: body surfaces or wing surfaces. Body surfaces are used for the fuselage and engine nacelles, and its shape is determined by its top and side view as well as different sections. Meanwhile, the wing surfaces are used for wings, lifting surfaces, and horizontal and vertical stabilizers. Its profile can be determined using a standard airfoil (i.e. NACA airfoil), defining your own airfoil or copying the one from the overlaid geometry.

14 AcBuilder The AcBuilder module allows building conventional aircraft geometries (one fuselage, one main wing, one horizontal tail, etc.) by defining its components and their dimensions. The mass and position of the fuel tanks, as well as the cabin parameters (volume, number of seats, pressure) can be specified which allows plotting the center of gravity of the different elements and the total one. Different technology parameters such as beam model, spar location and material properties can also be defined in preparation for the structural module NeoCASS. The output file is an “.xml” file, specifically created for CEASIOM, which is the input of the other modules.

Figure 6.5: AcBuilder’s user interface.

Weight and Balance The W&B module is used to calculate the weights of the aircraft as well as its total center of gravity and the moments of inertia. These calculations are done introducing the AcBuilder “.xml” file as an input and using a semi-empirical method. Depending on the aircraft size and type, different estimation methods, mainly based on statistical handbooks, are suggested (Howe, Torenbeek, Raymer, USAF and Cessna). The user is also able to set all of the weights or some of them manually.

Figure 6.6: User interface of the Weight and Balance module.

15 SDSA SDSA is CEASIOM’s module specialized in studying the stability and flying qualities of an aircraft. Different studies can be performed such as determining the eigenvalues of the system, thus finding the different dynamic flying modes (phugoid mode, short period mode, roll mode, etc.), finding the static margin, executing a flying maneuver, etc. As an input, SDSA needs all the aerodynamic coefficients (stability derivatives and control derivatives) as well as mass and geometric properties, information about the and power unit properties. All this information can be loaded separately in multiple text file structures or in a single XML file. This second option is the one used when using SDSA combined with other CEASIOM modules. It allows combining the information gotten from the rest of modules in an easy way, as all of the other modules output is given in XML format.

6.1.3 Digital DATCOM The Digital DATCOM is a computer program that implements the methods contained in the United States Air Force DATCOM, which allows estimating the stability and control characteristics of an aircraft for preliminary design applications. It calculates, in a rapid and economical way, the static stability, high-lift and control device, and dynamic-derivative characteristics. Moreover, a trim option is available that allows to compute the control deflection and aerodynamic data for aircraft trim at subsonic speed. The inputs for this program can be divided in 4 groups. In group I, the flight conditions and reference dimensions of the aircraft are defined. The second group contains the basic geometric parameters for a conventional configuration (body, wing and tail). Group III inputs define unconventional configurations or other configuration parameters (i.e. engines, flaps, control tabs). Finally, the inputs in group IV are used to control the execution of the case. Digital DATCOM was the first approach used for finding the aerodynamic coefficients of the chosen designs. Nonetheless, as DATCOM is based in experimental and semi-empirical data and supersonic business jets are something very new, it was decided to solve the flow around the aircrafts using CFD software.

6.1.4 MSES MSES is an airfoil design and analysis system developed by Dr. Mark Drela from the Department of Aeronautics and Astronautics at the MIT. Single and multi-element airfoil can be analyzed, modified and optimized for a wide range of Mach and Reynolds number. Problems such as shock-induced separation, shock waves or transitional separation bubbles can be solved. To represent the inviscid flow, the steady Euler equations in integral form are used; to represent the boundary layers and wakes, a compressible lag- dissipation integral method is implemented. Both flows are coupled through the displacement thickness of the boundary layer (δ*) and solved using a global Newton-Raphson method. One of the innovative features of this code is that it uses an intrinsic streamline coordinate grid which assumes that there is no convection across streamline cell faces. This turns the grid into an unknown; therefore the mesh is part of the solution and has to be stored continuously. This code has different programs which are used for different purposes. MSET is the grid and flowfield initializer. The inputs for this program are the files “blade.xxx” and “mses.xxx”. “Blade.xxx” contains the x-y coordinates of the airfoil while “mses.xxx” defines the runtime parameters. The output given by MSET is an “mdat.xxx” file which is the main solution state file. MSES itself is the flow solver, which needs the “mses.xxx” and “mdat.xxx” files as inputs and rewrites the solution on “mdat.xxx”. To be able to visualize the results, either as plots or coefficients, the MPLOT program has to be run. Finally, parameter-sweep calculations can be done using MPOLAR. In this case, apart from needing “mdat.xxx” and “mses.xxx” as inputs, another file determining the desired sweep has to be introduced (“spec.xxx”). To plot the results, PPLOT or SPLOT have to be used. A clear roadmap of MSES is shown in figure 6.7, including only the programs and data files that have been used during the realization of this Master Thesis.

16 Figure 6.7: MSES roadmap from "A User’s Guide to MSES 3.04"

6.1.5 Edge Edge is a CFD flow solver for unstructured grids of arbitrary elements (www.foi.se) developed by the Swedish Defence Research Agency (FOI). KTH, SAAB Aerosystems, TUB (Germany) and University of Britsol (UK) have helped in its development which started in 1997. In this case, Edge was used as an Euler solver to find out the aerodynamic coefficients of the chosen models. Three different files are needed as input: a “.ainp” file with the input values, the model’s volume mesh (“.bmsh” file) and a “.aboc” file with its boundary conditions; these two last files are obtained with SUMO. It is very important to define the projection of the forces (lift, drag and side force), which change depending on the angle of attack and side angle (equations 6.1, 6.2 and 6.3), as well as the point of reference to calculate the moments. The process of choosing a moment reference point will be explained in a later section.

L1 = sin α × (−1); L2 = 0; L3 = cos α (6.1)

D1 = cos β × cos α; D2 = sin β; D3 = cos β × sin α (6.2)

S1 = cos α × sin β × (−1); S2 = cos β; S3 = sin α × sin β × (−1) (6.3) Once everything is defined properly, the preprocessor has to be executed. The elements are discretized to control volumes surrounding each vertex and then control volumes are fused to coarser the grid cells (this will be used for multigrid). To improve the performance of the CPU with the cache memory, the nodes and edges are reordered, only in case cache reordering is previously selected. Finally, Edge has to be started either with a parallel or a sequential calculation.

6.1.6 ANSYS ICEM CFD ICEM is a meshing software developed by ANSYS that allows the user to import a geometry from a CAD program and fix it to produce a high quality surface or volume mesh. It includes mesh diagnostic

17 and interactive tools for editing the mesh. The obtained mesh can be exported to various formats that can be after introduced in computational fluid dynamics and finite element analysis solvers.

6.1.7 Tornado Tornado is a vortex lattice method for wings thought for conceptual design and educational purposes. It can solve the aerodynamic coefficients very fast by modelling the lifting surfaces as thin plates. This allows the user to get a first approximation of the effects of modifying the geometry without the time delays that entail the more accurate whole-body calculations. The code is implemented in MATLAB and developed by the Swedish Royal Institute of Technology (KTH), the University of Bristol, Linköping University and Redhammer Consulting Ldt. This program has been used to complete the aerodynamic database for our chosen SSBJs. The lifting surfaces of the aircrafts are needed as input, as well as the flying conditions. Tornado can calculate static cases or different sweeps and also other more complex cases as the trimmed aircraft polar point, unsteady cases, viscous drag estimations, etc.

6.1.8 GoCart GoCart implements NASAs CDF solver code (CART3D) in a simple and user friendly GUI developed by Desktop Aeronautics. It is used to perform inviscid aerodynamic analysis and is mainly thought for design purposes. It is divided in four sections: “preprocessor”, “volume mesh”, “flow solver” and “postprocessor”. In the preprocessor the geometry has to be introduced either using CART3D files “.tri”, RAGE input files or a “.stp”/“.stl” CAD integration file. The preprocessor checks that the model is watertight and that all its components intersect. Once this is done, the volume mesh is generated. The parameters of the mesh can be modified and the changes are quickly visualized. If everything works properly and cubes can be ran, the volume mesh will be generated and the user will pass to the flow solver section. Several parameters can be modified in the flow solver section. First, and maybe most important, the reference values (length, area, moment reference point) and flight conditions (Mach and angle of attack) need to be introduced. The value of these parameters affects greatly the results; therefore, it is crucial to use the correct ones. Some cases are more challenging than others and may require modifying the flow solver settings to obtain good convergence: lower the CFL number, lower the number of multigrid levels, use a more dissipative limiter, run first order, etc. Finally, when the user determines that a good convergence is obtained, the results can be visualized in the postprocessor. The aerodynamic forces and moments can be seen both in the aerodynamic and body frame. The distribution around the aircraft of other parameters (e.g. pressure coefficient, Mach number) can be observed in a 3D view of the model with a color scale. Additionally, Mach and alpha sweeps can be done once one calculation is completed.

6.1.9 RAGE RAGE is Desktop Aeronautics’ aircraft geometry generator. An aircraft can be easily implemented by defining its different components one by one (fuselage, wing, control surfaces, horizontal tail, vertical tail, etc.). The output file can be exported to a file extension which some CAD programs can read. Wings and wing-like components are defined determining the chord and airfoil of different sections. The fuselage is also defined by sections, specifying the type of shape and the variables defining it. Introducing control surfaces is quite simple, as they are characterized as wing-like components. When using GoCart to analyze the flow around an object, it is preferable to define this object in RAGE and not using other CAD programs. This way, problems will be avoided when using GoCart (more details are given in chapter 16).

6.2 Procedure Followed

The primary goal of this thesis is to find the early flying and handling qualities of a group of supersonic business jets as well as studying their stability. In order to do this, an reverse engineering process has

18 been followed, trying to determine the design decisions the designers made. The starting point was the existing conceptual designs which already had some control surfaces drawn on them. From there, a study of the static stability was done to rate the suitability of these surfaces and determine if changes had to be done. Once decided the proper size of the control surfaces to achieve good static stability characteristics, a dynamic stability study was conducted. The steps followed to achieve this goal are schematized in figure 6.8.

Figure 6.8: Box diagram showing the procedure followed to complete this thesis. The programs that were finally used are the ones inside the red box.

The first step consisted in defining the geometry of the aircraft. This was done using different programs depending on the type of input needed for the CFD code: SUMO, RAGE, AcBuilder and Tornado. Without a geometry, there is no way to start the process. Once we had a defined geometry, a surface and volume mesh had to be obtained for each model. SUMO and GoCart do their own meshes; ICEM can be used to modify the surface meshes obtained with SUMO. No mesh is needed for Tornado as it uses a vortex lattice method. To be able to run proper computational fluid dynamic calculations, it was necessary to calculate the center of gravity of the aircraft, this was done using W&B CEASIOM’s module. This module also allows to calculate the moments of inertia of the SSBJ which would be used later as part of the input for the SDSA module. Once all the different CFD calculations were done and the aerodynamic database built, all this information plus other parameters were introduced to the stability and control module of CEASIOM (SDSA) as an .xml file, obtaining as an output the flying and handling qualities of the vehicle. It is important to note out that, even though all the programs mentioned were used during the thesis, some of them were discarded as they were not the most convenient for the purpose of this study (will be explained later on in chapter 7 and section 11.1). The programs that were finally used to obtain the flying and handling qualities of the SSBJs are the ones inside the red box in figure 6.8.

19 Part II

Work Done

7 CAD Models

The three different aircraft configurations needed to be introduced into a CAD program to obtain a 3D model from which extract a mesh for the Computational Fluid Dynamics (CFD) calculations. With this aim, the program chosen to build the SSBJs was SUMO (Surface Modeler). To be able to model the desired aircraft configurations, the geometry of the jet was imported to SUMO using an “.stl” file by using the option “Load overlay geometry. . . ”. The “.stl” file was obtained differently in each case. For the low noise configuration of HISAC, the geometry was extracted from a mesh that had been generated during previous studies at KTH. A wind tunnel model of the LM1021 was found on the website of the American Institute of Aeronautics and Astronautics (AIAA) Sonic-Boom Workshop of January 2014 and was adapted using the 3D CAD design program CATIA from Dassault Systems. Finally, only the 3 views and some dimensions of the AS2 were available, so the model had to be done from scratch using CATIA. When trying to introduce the control surfaces into the SUMO models, a few problems aroused. Implementing the control surfaces directly with SUMO was quite challenging, therefore it was decided to use the software ICEM to deflect the surface mesh directly. This procedure involved an arduous task of reparation as, when deflecting the desired surface, the mesh ruptured and it had to be fixed node by node. This process had to be repeated for every specific deflection which was very time consuming. The next problem appeared when introducing the modified surface mesh into GoCart. If the mesh had not been properly repaired, which occurred more often than desired, GoCart was not able to create a volume mesh for it. For all these reasons, it was decided to take another course of action. GoCart permits deflecting surfaces very easily by defining a rotation axis via two points selected by the user. Unfortunately, the input file introduced in GoCart with the vehicle’s geometry has to be divided into its different components to be able to select the specific component that wants to be deflected (i.e. the control surfaces). This can be achieved using Desktop Aeronautics’ CAD software, RAGE. The RAGE models were built based on the SUMO models; on figure 7.1 (left side) the elevator surfaces can be distinguished as independent components of the aircraft (each component has a different color). To assure the water-tightness of the models, the RAGE files (“.input”) were exported to Cart3D files (“.tri”) before introducing them into GoCart.

7.1 Assumptions

Due to the fact that the amount of information available for these designs is scarce and that SUMO is a fairly simple modeler, some assumptions had to be made in order to be able to create the 3D models. For all the configurations, the engines were deleted in the model, as its inclusion did not add any benefit to our calculations. Nonetheless, for the LM1021, the tail is embedded in one of the engines

20 Figure 7.1: CAD models built with RAGE (left) and SUMO (right). From top to bottom: AS2, HISAC and LM1021.

21 therefore this one could not be simply removed. Instead, the fuselage was lengthened and the shape slightly modified so that the tail would lay on the fuselage without the need of including the shape of the engine. This way, calculation problems when using CFD were avoided. It was decided to simplify the wings as much as possible to be able to obtain a mesh. Therefore, planar wings with no camber and no twist were implemented (zero lift coefficient design to start with). The airfoils used for the wings and tails of all the models were NACA 66003 airfoils. The election of the airfoils is explained in detail in section 7.2.

7.2 Determination of the Wing’s Airfoil

The major problem when creating the 3D models was determining the wing airfoil. The profile for the HISAC design was extracted from the geometry available by using the SUMO option “Wing sections from overlay. . . ”. Unfortunately, the results obtained were not the desired ones; strange curves and edges appeared at the leading edge (LE). What SUMO does to copy the airfoil from an overlay is to use a reference profile with a thickness of 18% and project 120 points. As HISAC’s profile is basically a thin plate, only one point got projected to the LE (figure 7.2), making it impossible for SUMO to carry out a proper interpolation of this part of the airfoil. To be able to define the wing’s nose properly, more than 100 points would be needed to create the spline. SUMO’s code can be changed for it to be able to do this, but it would be useless as commercial CAD programs (i.e. CATIA, NX, etc.) would not be able to read the “.iges” or “.stp” files because they cannot open splines with more than 100 points.

Figure 7.2: Projection of reference profile (SUMO).

A similar problem was detected when working with the LM1021 model. In this case, SUMO was able to copy the overlay geometry quite properly (the nose definition was acceptable), but the LE was too sharp for SUMO to mesh it. To overcome this problem, some cuts were performed to the CATIA model obtained from the AIAA website in order to find the airfoils used and try to determine if any existing airfoil (i.e. NACA airfoil) was similar to it. Three different NACA airfoils were chosen to further study their aerodynamic characteristics and compare them to the real airfoil by using MSES. The details of this study can be found in chapter 8. Unfortunately, none of the studied NACA airfoils behaved like the airfoil extracted from the LM1021 CAD model. As for the Aerion AS2, the only information found with respect to the wings was that they were designed to create laminar flow around themselves. No specific details on the airfoils used were given. As a consequence of all these difficulties, an educated guess had to be done to determine the airfoil that would be used in the SUMO models. All the airfoils (in all the images available) seemed extremely thin and with little curvature. Experience determines that for supersonic leading edges, biconvex airfoils with a thickness of 2-3% at 50% of the chord should be used. On the other hand, for subsonic leading edges, very thin airfoils with a zero lift coefficient design are required. As already mentioned, SUMO has problems meshing very sharp leading edges (like the ones of a biconvex airfoil), therefore it was decided to use the NACA 66003 airfoil, which has a maximum thickness of 3% quite back in the airfoil, for all the cases.

22 8 Comparison of Airfoils using MSES

8.1 Objective

As already mentioned in chapter 7, a major problem was encountered when deciding the airfoil for the CAD models’ wings, especially for the LM1021, which will be the focus of this parallel study from now on. An airfoil could be obtained from the CATIA CAD model, but its geometric characteristics made it impossible for SUMO to mesh it, as the LE was too sharp. To overcome this matter, an airfoil 2D analysis was done using the CFD nonlinear viscous-inviscid code MSES. A comparison between the LM1021’s airfoil and similar airfoils was executed to try to find one that had resembling aerodynamic performance.

8.2 Chosen Airfoils

After performing several cuts to the wing of the CATIA model, it was determined that the airfoil was kept constant along the wing (figure 8.1). Therefore, the wing’s airfoils study was reduced to one airfoil. It was decided to compare this profile with NACA 4-digit airfoils, as they are easily defined with the maximum chamber, the maximum chamber position and the thickness. In accordance to the values obtained for the LM1021 airfoil, three different NACA airfoils where chosen for further study (figure 8.2 and table 8.1).

Figure 8.1: Different wing sections of the LM1021.

23 LM1021 NACA0002 NACA1502 NACA1503 Maximum chamber [%] 0.4 0 1 1 Maximum chamber position [%] 50 0 50 50 Thickness [%] 1.8 2 2 3

Table 8.1: Main characteristics of the chosen airfoils

Figure 8.2: NACA airfoils chosen for study

8.3 Procedure of Calculation

The first step consisted in initializing the grid and the “mdat.xxx” file by using MSET. Once this was done, calculations could be started using MSES. To be able to find a solution, it is necessary to start the calculation with a converged point or a point which is easy solvable (i.e. low Mach number and low angle of attack). For that reason, the first case to be solved was for M=0.5, α=0.5 and Re=4E6, which results were used to make an initial comparison. When analyzing the results obtained for the pressure coefficient distribution (figure 8.3), Mach number distribution (figure 8.4) and boundary layer thickness (figures 8.5 and 8.6) along the airfoil, it seemed that the NACA 1503 was the one with the closest behavior to the LM1021 airfoil. Although the aerodynamic coefficients (table 8.2) differed quite a lot, it was decided to do more calculations with these two airfoils in different regimes to keep comparing them.

LM1021 NACA0002 NACA1502 NACA1503 CL 0.29505 0.57554 0.37315 0.38201 CD 0.005306 0.04748 0.008681 0.005743 Cm -0.00876 -0.00995 -0.03186 -0.0329 L/D 55.606 12.122 42.983 66.513 CDv 0.005306 0.04748 0.008681 0.005743 CDw 0 0 0 0 CDf 0.003966 0.000997 0.003463 0.003931 CDp 0.001341 0.046483 0.005218 0.001812 dCL/dα 0.1606 0.0945 0.1146 0.1227 dCD/dα 0.001381 0.01986 0.005816 0.001379 dCm/dα -0.00719 -0.01962 0.0028 0.00138 Top Xtr 0.0099 0.0025 0.0034 0.0081 Bottom Xtr 0.9896 1 1 1

Table 8.2: MSES results for M=0.5 and α=2o

24 Figure 8.3: Distribution of pressure around airfoil (MSES results).

Figure 8.4: Mach number distribution around airfoil (MSES results).

25 Figure 8.5: Boundary layer thickness on top surface of the airfoil (MSES results).

26 Figure 8.6: Boundary layer thickness on bottom surface of the airfoil (MSES results).

It was decided to do two sweeps using MSES command MPOLAR. First, the angle of attacked was fixed to 0.5 degrees and the Mach varied. On the second sweep, the Mach was fixed to 0.5 and this time α was the varying parameter. This way we were able to figure out the divergence Mach number and the polar curves of the studied airfoils (figure 8.7).

8.4 Conclusions

MSES has some difficulties calculating the aerodynamic coefficients of the LM1021 airfoil for high angles of attack (> 4 degrees). Most probably, this is due to the fact that it is a supersonic airfoil which normally cannot fly at high α’s. Even with the lack of data for the Lockheed Martin’s airfoil, it is obvious from the polar curves that this airfoil and the NACA 1503 have a fairly different behavior. From the Mach sweep, it can be concluded that the LM1021’s airfoil divergence Mach number is around 0.8. It seems that the divergence Mach for the NACA 1503 is also around 0.8, but MSES was not able to calculate the drag coefficient for higher Mach numbers in this case, so it cannot be assured. Due to all the facts explained above, it was decided that no NACA airfoil from the ones studied could be used for our CAD models, as their properties were not similar to the ones of the LM1021’s airfoil extracted from the CATIA model. Further studies could have been done using MSES and other standardized airfoils, but MSES offers many limitations for supersonic calculations and it was decided to base the airfoil decision in experience.

27 Figure 8.7: Mach number and angle of attack sweep for LM1021 airfoil and NACA 15003 (MSES results).

9 Finding the Mean Aerodynamic Chord

The mean aerodynamic chord (MAC) of an aircraft is used to normalize the aerodynamic forces to obtain the lift, drag and pitching moment coefficient. It is also used to figure out the static margin of an aircraft and make sure it is always stable. Therefore, it is very important to know the MAC of the studied SSBJs. In the case of a tapered or delta wing, the MAC is easily found graphically (figure 9.1). Unfortunately, none of the airplanes that are being studied in this thesis have a tapered or delta wing, they all have multi-crank wings. To find the MAC of a generalized multi-crank wing, ESDU 76003 has been used. The results are shown in table 9.1.

m+1 P 2 2 ci−1(1+λi+λi )ηi 2 i=1 si−si−1 ci • Aerodynamic mean chord: c = being ηi = and λi = 3 mP+1 b/2 ci−1 ci−1(1+λi)ηi i=1 2 2 2 c 2 η1(1+λ1+λ1)+λ1(1−η1)(1+λ2+λ2) c1 ct - For a single-crank wing: = being λ1 = and λ2 = c0 3 η1+λ1+λ1λ2(1−η1) c0 c1

• Chordwise position of MAC (from wing apex): m+1 i−1 A P P c b2 x1/4 = 12 [ ηici−1(3(1 + λi) ηj tan ∆0,j + (1 + 2Λi)ηi tan ∆0,i)] + 4 being A = S and ∆n,i i=1 j=1 th the sweepback of the n chordline between spanwise stations si−1 and si - For a single-crank wing: A 2 1 c x = [η1(η1(1 − λ1) + 3λ1λ2(1 − η1)3η1) tan ∆0,1 + λ1(1 + 2λ2)(1 − η1) tan ∆0,2] + 1/4 12 4 c0

28 AS2 HISAC LM1021 MAC [m] 8.2603 9.8427 16.2533 x1/4 [m] 1.49 9.8382 22.3169

Table 9.1: Mean aerodynamic chord of the SSBJs

Figure 9.1: Method to find MAC of a tapered or delta wing.

10 Estimation of the Center of Gravity and Moments of Inertia

In order to be able to carry out the CFD calculations properly, it was necessary to find the center of gravity (CG) of the aircrafts in advance. The moments created in a vehicle are dependent on the position of its CG, therefore, any calculations done without introducing properly the CG would be incorrect. As for the moments of inertia, they are essential when estimating the behavior of the SSBJs using SDSA. To obtain these values, CEASIOM’s module Weight and Balance (W&B) was used. Nonetheless, prior to using it, it was necessary to build the CAD models of the aircrafts using CEASIOM’s CAD software AcBuilder, as it is a necessary input for W&B.

10.1 AcBuilder’s Models

As already mentioned, the Weight and Balance module only accepts as an input the “.xml” file created by AcBuilder. There is no other way of introducing the geometry into CEASIOM, therefore, building the models with AcBuilder became necessary (figure 10.1). This CAD modeler has some limitations: • Only conventional configurations can be introduced. The components of the aircraft are already determined and none can be added.

• The fuselage cannot be defined in detail. It is divided in four parts (nose, for-fuselage, aft-fuselage and tail) and the aft-fuselage section is maintained constant.

• The wing’s airfoil has to be selected from a list given, which is not too extended.

A very tricky part of building the models was determining the size and location of the fuel tanks. No information about this was available for the chosen SSBJs, so an estimated guess had to be done. It was basically a guess and error process, in which the position and volume of the tanks was modified until the local and total centers of gravity obtained seemed reasonable.

29 Figure 10.1: Aircrafts built in AcBuilder. Left to right: AS2, HISAC and LM1021.

10.2 Estimation using Weight and Building Module

Once the input “.xml” file is chosen, the W&B module runs different semi-empirical methods to calculate the estimated weights of the aircraft: structure (wing, tail, fuselage, etc.), systems (electric system, flight control, avionics, etc.), total empty weight, payload, fuel weight and total weight. Each method of calculation is supposed to be accurate for a certain type and size of aircraft. However, as supersonic business jets are very uncommon, this approach of choosing a method was not appropriate. Instead, as the empty weight, fuel weight and maximum take-off weight of the Aerion AS2 and the Hisac low noise configuration were known, the method which obtained the most similar values was selected. In both cases, it was the Torenbeek method which is initially thought for big transport aircrafts with take-off weights above 5700 kg and with design dive speeds above 250 knots. Once the method was selected, the values of the EW, FW and MTOW were modified to make them coincide with the known real values. The final weight distribution as well as the different centers of gravity and moments of inertia, can be found in tables 10.1, 10.2 and 10.3

Different Weights [kg] AS2 HISAC LM1021 Wing 4796.85 5193.10 6354.44 Horizontal Tail 522.58 693.30 Vertical Tail 265.62 Fuselage 6747.76 10910 11606.64 Landing Gear 1617.65 1932.37 2331.66 Total Structure 13950.46 18035.48 20986.04 Fuel System 288.67 281.40 291.79 Flight Control 473.15 535.35 577.73 Avionic 937.73 984.41 1107.67 Electric System 566.48 443.41 790.13 Air Conditioning 237.76 190.91 647.81 Furnishing 550 400 500 Total Systems 3053.78 2835.48 3915.12 Total Empty Weight 22588 25208 24901.16 Payload 1089 792 990 Fuel 28486 27300 29000 Total Weight 52163 53300 54890.80

Table 10.1: Weight breakdown.

30 [m] AS2 HISAC LM1021 CG at Empty Weight X 31.6257 24.9598 32.4578 Y 0 0 0 Z -0.0644 -0.1946 0.01 CG at Zero Fuel Weight X 29.1529 24.5975 32.2432 Y 0 0 0 Z -0.0710 -0.1670 0.0365 CG at Take-Off Weight X 29.9184 26.8858 33.4206 Y 0 0 0 Z -0.2537 -0.1030 0.1101

Table 10.2: SSBJs’ total center of gravity for different weights.

Moments of Inertia AS2 HISAC LM1021 Ixx [kgm] 479615.39 142897.00 514486.46 Iyy [kgm] 1060296.24 4229928.44 6142560.28 Izz [kgm] 1532515.28 4323392.95 6617113.74 2 Ixz [kgm] 16011.30 1888.56 9662.70 2 Ixy [kgm] 0 0 0 2 Iyz [kgm] 0 0 0

Table 10.3: SSBJs’ moments of inertia. 11 Building the Aerodynamic Database

In order to be able to study the stability and performance of an aircraft it is essential to build a database with all the aerodynamic coefficients for certain flight conditions. This has been done using different CFD codes, one solves the flow around the aircraft using Euler equations (inviscid flow) and the other one uses the Vortex Lattice Method (VLM). The fact of using Euler or VLM to solve the flow around the aircraft gives low-fidelity results, but this is not a major concern. Many of the inputs used for the CFD codes are based in approximations and educated guesses due to the little information that is known about the chosen SSBJs, which means that the aerodynamic coefficients found are approximations (even if solved with higher fidelity methods). To study static stability during cruise phase, only a few calculations where needed for each model and they were performed using GoCart. An alpha sweep from 0 to 6 degrees was performed for different elevator deflections (0, -1, -3 and -5 degrees) at Mcruise. The control deflections were done directly in GoCart. As already mentioned in chapter 7, the input file used for GoCart has been built with Desktop Aeronautics’ aircraft geometry generator (RAGE), which divides the geometry into different component, being the control surfaces independent components. The deflection of the control surfaces is done with a geometrical rotation around an axis, defined during the preprocessor section of GoCart. As for studying the dynamic stability and behavior of the vehicles, a broader aerodynamic database was necessary, including situations with non-zero angular velocities. Nowadays, GoCart is not able to implement rolling, yawing or pitching speeds into its calculations, therefore, another program had to be used for these cases. The chosen code was Tornado, which offers good approximations quickly, allowing the user to carry out many calculations in a very short time. Two different matrices had to be build, an aerodynamic matrix containing the stability derivatives (structure shown in table 11.1) and the control matrix with the control derivatives (structure shown in table 11.2). In both cases the angle of attack was varied from -2 to 6 degrees every one degree and the Mach number modified from the subsonic (0.2, 0.4, 0.6) to the supersonic region (1.1, 1.2, 1.3 and 1.4 for the AS2; 1.15, 1.3, 1.45 and 1.6 for the LM1021; 1.2, 1.4, 1.6 and 1.8 for HISAC) avoiding the nonlinearities of the transonic regime. As for the side-slip angle it was varied from -4 to 4 degrees every 2 degrees, and the rolling, yaw and pitch speed

31 from -20 to 20 deg/s with steps of 10 deg/s. The control surfaces deflections studied were the following: o o o δe = (−5, −3, 3, 5) , δr = (−2, 2) and δa = (−2, 2) .

α M β q p r CL CD Cm CY Cl Cn X X X - - - X X X X X X X X - X - - X X X X X X X X - - X - X X X X X X X X - - - X X X X X X X

Table 11.1: SDSA aero matrix structure

α M δe δr δa CL CD Cm CY Cl Cn X X X - - X X X X X X X X - X - X X X X X X X X - - X X X X X X X

Table 11.2: SDSA control matrix structure

It is important to point out that Tornado is only valid for subsonic calculations. When the flow-speed is high enough to allow compressibility effects, the Prandtl-Glauert correction is used (e.g. equation 11.1). Unfortunately this rule cannot be applied to supersonic flows as the result would involve imaginary numbers. SDSA needs a complete aerodynamic database to work but GoCart is not able to include rotational speeds (p, q, r) to the calculations. Therefore, Tornado had to be used to perform the p/q/r calculations for the supersonic regime but without using the aforementioned correction. Due to the lack of time, the cases with rudder and aileron deflections were also calculated with Tornado instead of GoCart. This implies that the aerodynamic coefficients found for these specific cases are incorrect. Nonetheless, it does not pose a problem because the focus of the study is the longitudinal behavior which only depends on the α-sweep and the elevator deflection cases, which were calculated appropriately.

Cp,0 Cp = (11.1) p 2 1 − M∞ All the computational fluid dynamic calculations have been done using the most favorable center of gravity as the reference point for calculating the moments. For the three studied models, the center of gravity which is closer to the nose is the one corresponding to zero fuel weight conditions.

11.1 Why Use GoCart Instead of Edge?

Traditionally, at the Aerodynamics Division of the Aeronautical and Vehicle Engineering School of KTH, the CFD code Edge has been used. Nonetheless, there was an opportunity to use the recent software GoCart that implements NASA’s CFD code Cart3D, thought for solving supersonic cases. It was decided to compare both programs to figure out which one would fit better the purpose of this study. In order to be able to compare the results obtained it was first necessary to experiment and play around with GoCart, as no one from the department had used it before. It was found out that when spec- ifying y-symmetry in the meshing part, the area that had to be later introduced in the flow solver section had to be half of the actual surface area. Also, when y-symmetry was indicated, the lateral/directional coefficients (CY , Cl and Cn) would not be accurate. Therefore, it was concluded that using symmetry in GoCart was only trustworthy to study longitudinal aspects of the aircrafts. The major differences between GoCart and Edge are the following: • Edge requires the user to introduce the volume mesh as an input file. On the other hand, GoCart creates its own volume mesh, requiring the surface mesh as an input. In this case, the volume mesh needed for Edge was done using SUMO, while the surface mesh necessary for GoCart was done with RAGE.

32 • Edge uses a different reference length to calculate the lateral/directional coefficients (CY , Cl, Cn) and the longitudinal coefficients (CL, CD and Cm) while GoCart uses the same one. This might be one of the reasons that causes the differences on the lateral/directional coefficients that can be observed in table 11.3.

• At least for supersonic cases, GoCart calculates the flow around the body around 70% faster than Edge. A calculation that takes around 1 hour and a half to be solved using Edge, can be solved in about 25 minutes with GoCart.

• GoCart offers the possibility of performing an α sweep or Mach sweep automatically after solving one first case. Edge does not have this option which forces the user to be setting the cases one by one, which is very time consuming.

The main objective of the thesis is to study the longitudinal stability and controls of the chosen SSBJs. GoCart offers accurate longitudinal aerodynamic coefficients much faster than Edge, therefore, it was decided to use GoCart to create the aerodynamic database.

AS2 HISAC LM1021 GoCart Edge GoCart Edge Difference [%] GoCart Edge Difference [%] GoCart Edge Difference [%] Inputs Length Cref 8.26 8.26 9.84 9.84 26.19 26.19 Area Sref 125 125 139 139 150 150 Bref 21 19.1 17.4 Mom X IXMP (X) 26.95 26.95 22.53 22.53 27.06 27.06 Mom Y IXMP(Y) 0 0 0 0 0 0 Mom Z IXMP(Z) 1 1 0 0 1 1 Outputs CL CL 2.5128E-01 2.4729E-01 -1.61 1.1822E-01 1.1797E-01 -0.21 2.7326E-01 2.6395E-01 -3.53 Cy CC = −Cy 4.6575E-02 5.1859E-04 -8881.15 8.0000E-06 1.6203E-05 50.63 -1.2760E-02 -5.2549E-06 -242720.99 CD CD 2.5514E-02 2.5060E-02 -1.81 9.5870E-03 9.5967E-03 0.10 2.8919E-02 2.7470E-02 -5.27 Cl(Rolling) Cl -1.2675E-01 -1.8543E-04 -68255.71 -1.6000E-05 -4.5410E-06 -252.35 -4.0277E-02 5.6891E-05 70896.79 Cm(P itching) Cm -8.6766E-02 -8.9304E-02 2.84 -7.2525E-02 -7.2639E-02 0.16 -8.3120E-02 -7.9600E-02 -4.42 Cn(Y awing) Cn -2.7087E-02 3.9976E-04 6875.82 3.0000E-06 -6.2735E-06 147.82 3.0990E-03 -2.7790E-05 11251.49

Table 11.3: Aerodynamic coefficients obtained with Edge and GoCart for M = Mcruise and α = 3deg

11.2 Effects of Geometry, Mesh and Calculation Methods in GoCart’s Results

11.2.1 Different Geometries As already mentioned, when implementing the surface controls in the aircrafts, it was necessary to use Desktop Aeronautics program RAGE, as it offered an easier way of deflecting those surfaces. On the other hand, RAGE has some limitations when building the models. The NACA 66003 airfoil could not be used for the wings and tails as only NACA 65-Series are offered; a NACA 65003 was used instead. When building the fuselage, also done by sections, the original geometry cannot be overlapped like in SUMO (which offers the option of adjusting manually your section). Therefore, all fuselage sections were estimated to ellipses. These differences in the models might cause variations of the aerodynamic coefficients obtained with GoCart. To figure out if this happened or not, the SUMO and RANGE models were solved using the same calculation method and the results were compared graphically.

AS2 The lift and drag coefficient completely coincide, but the moment coefficients show a significant difference (figure 11.1). The rolling and yawing coefficient of the RAGE model is not zero, like in the SUMO model, but it can be approximated to zero as the values are of order (-3) and (-4). With respect to the pitching moment coefficient, as the angle of attack increases the difference between the models also increases. This affects notably the angle of attack at which the airplane is trimmed; the RAGE model has higher αtrim.

33 Figure 11.1: Aerodynamic coefficients of AS2 for different geometries.

34 Figure 11.2: Aerodynamic coefficients of HISAC for different geometries.

35 HISAC In this case, the difference of the CL, CD and Cm between the SUMO and the RANGE model increase as the angle of attack increases (figure 11.2). The values obtained with the RANGE model for CL and CD are a little bit lower, but the difference can be disregarded. As for the pitching coefficient, both lines intersect the x-axis on the same point but the SUMO model’s line is steeper. This means that the trimming angle of attack is not affected by the difference in geometries, although the SUMO model is more statically stable than the RANGE model. As for the other moment coefficients, the yawing coefficient of the RAGE model can be approximated to zero (value for the SUMO model) but the rolling moment values obtained for the RAGE model are not negligible. Therefore, the SUMO and RAGE model are not comparable in this sense.

LM1021

Figure 11.3: Aerodynamic coefficients of LM1021 for different geometries.

No noticeable differences can be found between the SUMO and RANGE model of the LM1021 (figure 11.3). The lift, drag and pitching coefficients agree for all the angles of attack studied. The rolling and yawing coefficients of the RAGE model are not zero, as for the SUMO model, but they can be approximated to zero because they have a magnitude of order (-4) and (-5).

36 11.2.2 Different Meshes When working with CFD programs, it is extremely important to generate a good mesh of the object that wants to be studied. A good definition of the geometry is needed to obtain accurate results but if the mesh is not good enough, the obtained results will not be valid. GoCart creates the volume mesh automatically after defining some parameters: maximum number of refinements, number of buffer cell layers, number of multigrid levels, etc. To be sure that the obtained mesh was acceptable, a mesh refinement study was conducted for the Aerion AS2 and the HISAC model (table 11.4 and figure 11.4).

AS2 HISAC Max number of refinements 14 10 14 11 10 Number of buffer cell layers 3 3 3 3 3 Maximum number of hexes -1 -1 -1 -1 -1 Angle (deg) threshold for refinement 5 5 5 5 5 Additional refinement levels at sharp features 1 1 1 1 1 Number of multigrid levels 3 3 3 3 3

Table 11.4: Mesh parameters

Figure 11.4: Meshes obtained with different number of refinements. Top (from left to right): HISAC 14, HISAC 11, HISAC 10. Bottom (from left to right): AS2 14, AS2 10.

As it can be seen in figures 11.5 and 11.6, the aerodynamic coefficients obtained with different mesh refinements are not so different. Nonetheless, when dealing with static longitudinal stability, the value of the trim angle of attack (represented with crosses on the “Cm vs α” graph of figure 2) is very important. For example, a change of sign represents the difference between having a “nose-up” or “nose-down” aircraft during cruise. Although the difference on Cm is not big, it does change significantly the value of alpha trim, affecting greatly the analysis. That is the reason why we want a refined mesh, to obtain the most accurate results.

11.2.3 Different Calculation Methods When implementing the control surfaces in RANGE, GoCart has problems solving the flow around the aircrafts. As the complexity of the problem that has to be solved increases, it is more difficult to obtain a good convergence. To overcome this issue, a checklist elaborated by Desktop Aeronautics for poor convergence was followed. The first step was to reduce the CFL as low as 0.5. This would not work, therefore a more dissipative limiter was used (MinMod(5) which is the most robust of the ones offered). The problem would not converge with these modifications, so the next step was to try solving it using a 1st order method instead of a 2nd order method. Finally, the program found a converged solution, although it took very long as the CFL was extremely low. By increasing again the CFL, the problem would still converge and in a much faster time (around half the time it took in the previous case).

37 Figure 11.5: Aerodynamic coefficients obtained for the AS2 with different mesh refinement.

Figure 11.6: Aerodynamic coefficients obtained for the HISAC with different mesh refinement.

38 Nonetheless, as a 1st order method had to be used to find good convergence, the accuracy of the results was questionable. First order methods can be used to compute a steady-state solution reliably and quickly on almost any mesh, but normally the accuracy threshold desired is not reached. To try to validate the obtained results, two different methods of calculation were compared (a 2nd order method and a 1st order method). The geometry used for these calculations were the SUMO models of the studied aircrafts, as they presented no problems of convergence. Doing a comparison of the different methods of calculations also allowed us to find out if the differences we obtained between the SUMO models and the RANGE models were due to the mathematical model being used or the geometry itself.

AS2

CFL Multigrid Levels Flux Function Limiter Cut-cell Gradient Suppression Method 1 1.4 3 VanLeer(0) VanLeer(2) 1.0 (2nd order) Method 2 1.4 3 VanLeer(0) VanLeer(2) 0.0 (1st order)

Table 11.5: Different calculation methods used for the Aerion AS2 model.

Figure 11.7: Aerodynamic coefficients of AS2 for different methods of calculation.

As it can be seen in the graphs of figure 11.7, the method of calculation (table 11.5) affects mainly to the rolling and yawing moment coefficient. They seem to follow a similar trend but the values are not

39 exactly the same (mainly for the yawing moment). Nonetheless, the values are of order (-5), therefore, it can be assumed that the rolling and yawing moments are zero.

HISAC

CFL Multigrid Levels Flux Function Limiter Cut-cell Gradient Suppression Method 1 1.4 3 VanLeer(0) VanLeer(2) 1.0 (2nd order) Method 2 1.4 3 VanLeer(0) MinMod(5) 0.0 (1st order)

Table 11.6: Different calculation methods used for the HISAC model.

Figure 11.8: Aerodynamic coefficients of HISAC for different methods of calculation.

As before, the yawing and rolling moment coefficients are affected by the calculation method (table 11.6 and figure 11.8). In this case, the trend is not even similar; there are huge disparities between results. Nevertheless, as it happens in the previous case, the magnitude of these coefficients is of order (-5), therefore they can also be considered zero.

LM1021 As in the previous case, the lift, drag and pitching moment coefficients trend is kept with almost exact values (figure 11.9). The trends obtained for the rolling and yawing coefficient for each method are

40 Figure 11.9: Aerodynamic coefficients of LM1021 for different methods of calculation.

41 CFL Multigrid Levels Flux Function Limiter Cut-cell Gradient Suppression Method 1 1.4 3 VanLeer(0) VanLeer(2) 1.0 (2nd order) Method 2 1.4 3 VanLeer(0) MinMod(5) 0.0 (1st order)

Table 11.7: Different calculation methods used for the LM1021 model.

completely different, but, as before, both results are of the same order of magnitude (-5) and the values can be approximated to zero.

11.2.4 Conclusions The method of calculation used with GoCart does not affect the resultant aerodynamic coefficients, as long as the result has converged. On the other hand, a slight difference in the geometry can affect the obtained results. This is something which was expected, but the fact that the differences were very subtle, indicate that the RANGE model and the SUMO model are comparable. As for the meshes, the more refined the best. Therefore, it was decided to run all the calculations using the RANGE models with each case’s method 2 of calculation and with a mesh refinement of 14. These conclusions greatly apply to the CL, CD and Cm. The similarities between the Cn and Cl are not so obvious, as many approximations need to be done. The lateral-directional performance of an aircraft is based on the yawing and rolling moment coefficients, amongst others, which are not very trustworthy in these calculations. Nonetheless, as the scope of the thesis is for longitudinal performance, this is no problem.

12 Longitudinal Static Stability

12.1 Theoretical Background

12.1.1 Neutral Point The neutral point (NP) is the point at which the variation of the pitching moment with respect to the angle of attack (α) is zero. If the center of gravity (CG) is situated before this point, the aircraft is said to be statically stable; if disturbed, a moment will be created that will return the aircraft to its original angle of attack, the one prior to the disturbance. If, on the other hand, the CG is located after the NP, active inputs to the control surfaces will be required to maintain a stable flight, hence the aircraft is statically unstable. It is extremely important to be aware of the location of the center of gravity of the aircraft and to know how aft it can be to retain stability. The behavior of an aircraft depends on the location of the CG. In some cases, aircrafts are designed to have static instability so that maneuverability is benefited. A statically unstable airplane, such as a fighter, has a much higher maneuverability than a conventional commercial airplane, as a slight disturbance drives away the vehicle from its original speed and orientation. For an aircraft to be statically stable, the change of pitching moment coefficient with respect to alpha

(Cmα ) must be negative. If the aircraft has a positive Cmα , the plane will be statically unstable. This can be very easily observed in a Cm vs. α graph (figure 12.1). If the line has a negative slope, the aircraft is statically stable. It will be unstable if the slope is positive and neutrally stable if it has no slope (horizontal line).

42 Figure 12.1: Static stability of an aircraft determined by the derivative of Cm with respect to α

12.1.2 Static Margin

The static margin (Kn) of an aircraft is the distance between its neutral point and its center of gravity normalized by the mean aerodynamic chord (MAC) (equation 12.1). This parameter is the basis for estimating the handling qualities of the vehicle. A positive static margin means that the aircraft is stable.

xNP xCG dCm Kn ≡ − = − (12.1) MAC MAC dCL

12.1.3 Trimming Conditions For a given flight condition, an aircraft is trimmed when there is an equilibrium of moments. In other words, the total pitching moment around the center of gravity must be zero for an aircraft to fly in a steady condition. This is especially crucial during the cruising phase of the flight mission, to reduce the pilot’s inputs as much as possible. The trimming point varies with the elevator deflection, as it is dependent on the lift coefficient produced by the airplane. For every elevator deflection, there is only one trimming point which can be found plotting the total pitching moment coefficient against the lift coefficient (figure 12.2). The angle of attack correspondent to this trimming point is the trimming angle of attack and determines if the aircraft flies nose-up or nose-down during steady flight.

Figure 12.2: Determining the trimming point.

43 12.2 Analysis of the SSBJs

The static margin and the neutral point of the aircrafts has been found using equation 12.1 and the aerodynamic coefficients calculated with GoCart for elevator deflections of 0, -1, -3 and -5 degrees. Table 12.1 shows the neutral point of the business jets and the static margin depending on the position of the center of gravity. All the SSBJs are stable under all weight conditions except the AS2 at empty weight. Nonetheless, this does not pose a problem as the aircraft will never be flying under these conditions. There will always be fuel left in the deposits which never gets consumed and some payload will be onboard (even if it is just the crew). It is important to point out that the static margins obtained for the LM1021 and the HISAC at empty weight and zero fuel weight conditions are disturbingly high, specially for the HISAC model. A static margin higher than 15% of the mean aerodynamic chord means that the aircraft is too stiff or, in other words, not easily maneuverable. This can be solved by moving the location of the center of gravity towards the tail (for example, studying the location of the fuel tanks), always being xCG < xNP to assure the stability of the aircraft.

Static Margin [% MAC] xCG @ EW [m] xCG @ ZFW [m] xCG @ TOW [m] xNP @ EW @ ZFW @ TOW AS2 31.6257 29.1529 29.9184 30.0106 -19.55 10.38 1.12 HISAC 24.9589 24.5975 26.8858 27.6532 27.37 31.05 7.80 LM1021 32.4578 32.2432 33.4206 35.3169 17.59 18.91 11.67

Table 12.1: Neutral point and static margin for each SSBJ

When an aircraft is flying at cruise conditions, it is desired for it to fly nose up. This means that the angle of attack in trimming conditions (when the plane flies in a straight attitude without control actions) must be positive. This occurs for the AS2 without even having to deflect the elevators at all. As for the HISAC model, a negative deflection of 1 degree is required while the LM1021 will not be able to achieve nose up cruising in any case (with the deflection angles studied). The second aspect which has to be in mind when studying cruise conditions is the lift to drag ratio obtained with the trimming angle of attack. A good aircraft design would have a L/D at trimming conditions close to the maximum L/D point. The LM1021 and specially the AS2 follow this design condition. On the other hand, a very poor lift over drag ratio is achieved with the HISAC model. All these conclusions have been extracted from table 12.2

Elevator deflection αtrim L/Dtrim α(L/D)max L/Dmax AS2 0 1.931 9.3259 2.7259 9.8443 -1 2.7669 9.782 2.8415 9.7853 -3 4.5548 8.6375 2.9888 9.4703 -5 6.2613 7.2491 3.1958 8.9703 HISAC 0 -0.28713 -1.9953 2.5336 11.993 -1 0.11564 0.61229 2.709 11.707 -3 0.92129 3.7237 3.2468 10.615 -5 1.7288 5.2107 3.899 9.2412 LM1021 0 -1.0697 12.603 0 13.572 -1 -0.96938 12.48 0 13.426 -3 -0.76172 11.91 0.1904 12.884 -5 -0.55012 11.096 0.438 12.129

Table 12.2: Trimming conditions when changing elevator deflection

12.3 Optimizing the Elevators’ Size

The elevator is the control surface that controls the longitudinal behavior of the aircraft by modifying the pitching moment. To optimize its size for each aircraft, two main parameters are going to be studied:

44 the angle of attack and the lift over drag ratio obtained for trimming conditions when flying during cruise phase with different elevator deflections. A positive αtrim has to be achieved with a L/D ratio close to the maximum L/D ratio given by the vehicle. The effectiveness of the elevator is measured by inspecting the change of lift and pitching moment when deflecting this control surface (dCL/dδe and dCm/dδe respectively).

12.3.1 First Iteration AS2 As already seen in section 12.2, good values of α and L/D are obtained for trimming conditions. To try to obtain better values of lift versus drag, the size of the elevator is increased in the first iteration. It can be seen in table 12.3 that augmenting the size of the elevators of the AS2 model does not benefit the design. The lift over drag ratio obtained for trimming conditions is reduced (especially for higher elevator deflections) which is a non-desired effect. For this reason, it is decided to leave the initial design untouched, as the trimming parameters are favorable (nose-up cruising and L/D close to maximum L/D).

2 Elevator’s surface area [m ] δe αtrim L/Dtrim α(L/D)max L/Dmax dCL/dδe dCm/dδe AS2 (v1) 6.64 0 1.931 9.3259 2.7259 9.8443 3.6002e-3 -8.0323e-3 -1 2.7669 9.782 2.8415 9.7853 -3 4.5548 8.6375 2.9888 9.4703 -5 6.2613 7.2491 3.1958 8.9703 AS2 (v2) 8.66 0 1.9093 9.3046 2.7332 9.8279 4.5450e-3 -1.0645e-2 -1 2.9986 9.7505 2.6449 9.8173 -3 5.2579 8.0888 2.9786 9.3388 -5 7.4748 6.9787 3.3593 8.6921

Table 12.3: First iteration of AS2 elevator’s optimization

HISAC The values obtained for the L/D ratio for the HISAC model at trimming conditions are extremely poor for the initial design. Deflecting the elevator in a negative direction increases the lift over drag ratio but the resulting numbers are still far away from the maximum L/D that can be obtained. To try to increase the L/D ratio of the aircraft, the effect of adding another lifting surface (i.e. a canard) is studied. It must be noted, that the center of gravity is affected by the addition of a canard. Nonetheless, this effect has not be taken into account in the calculation due to problems with the W&B CEASIOM’s module. For some unknown reason, when adding the canard to the AcBuilder model, the weights obtained for the wings would be an infinite number. As it can be seen in figure 12.3, the canard barely affects the lift and drag of the aircraft but does modify the pitching moment coefficient. The variation of Cm with respect to the angle of attack diminishes when adding a canard, therefore, the trimming conditions of the vehicle (when the pitching moment is zero) are altered. In this case, the objective of adding a canard to the initial design was to obtain higher values of the lift over drag ratio for trimming conditions. This goal is achieved for elevator deflections of -3 and -5 degrees (table 12.4), although the increase of L/D is not extremely significant and it is still way to far apart from the maximum value that could be reached. Taking into account these observations, it seems that adding a canard is the right way of achieving higher L/D ratios in cruise conditions but that the design can still be improved, most probably by making the canard bigger and adding control surfaces to it.

LM1021 When increasing the elevator’s area, the L/D ratio is affected (table 12.5). As the elevator deflection increases, L/D decreases mainly for low angles of attack (< 2 degrees). This diminishing of the L/D

45 Figure 12.3: Aerodynamic coefficients obtained for HISAC with canard (v2) and without a canard (v1) ratio is not due to an increase of the drag coefficient, which might have been the initial hypothesis, but due to a decrease of the lift coefficient. All this statements can be clearly observed in figure 12.4. Nonetheless, although the L/D ratio diminishes when increasing the surface area of the elevators, a positive trimming angle of attack is achieved for a δe of -5 degrees. The next step would be increasing again the size of the elevators to try to achieve a positive trimming angle of attack for lower elevator deflections which could give a higher L/D ratio than the one accomplished right now (> 10.09).

12.3.2 Second Iteration HISAC With a bigger canard, a considerably higher L/D ratio is achieved for trimming conditions, as can be seen in table 12.4. When the elevator deflection increases (in the negative side), the L/D ratio obtained also increases, although the maximum L/D decreases due to trim drag. For -5 degrees deflection, L/D = 7.884, which is a substantial improvement from the L/D = 5.2107 obtained with the first version of the aircraft and L/D = 6.4276 obtained with a smaller canard. Due to lack of time, no more optimization loops will be performed on the HISAC. From now on, the study will focus only on the third version which offers the best L/D ratio from all the cases studied. It is noted that future work should be carried out on this aircraft. Bigger canards should be evaluated as well as deflecting the canard as part of the elevator deflection.

2 2 Elevator’s surface area [m ] Canard surface area [m ] δe αtrim L/Dtrim α(L/D)max L/Dmax dCL/dδe dCm/dδe XNP Static margin HISAC (v1) 29.84 0 0 -0.28713 -1.9953 2.5336 11.993 5.1870e-3 -3.9696e-3 27.7292 0.318172 -1 0.11564 0.61229 2.709 11.707 -3 0.92129 3.7237 3.2468 10.615 -5 1.7288 5.2107 3.899 9.2412 HISAC (v2) 29.84 2.88 0 -0.62095 -5.7795 2.5519 11.902 5.1835e-3 -3.9573e-3 26.9418 0.238174 -1 -0.09221 -1.3081 2.7349 11.585 -3 0.97878 3.9851 3.2752 10.525 -5 2.0514 6.4276 3.9261 9.1896 HISAC (v3) 29.84 4.51 0 -1.1624 -12.569 2.5887 11.766 5.1750e-3 -3.9604e-3 26.2608 0.16899 -1 -0.41216 -4.5651 2.7647 11.492 -3 1.0872 4.5651 3.3012 10.462 -5 2.5829 7.884 3.9483 9.1563

Table 12.4: HISAC elevator’s optimization

46 Figure 12.4: Aerodynamic coefficients obtained for LM1021 for different elevator sizing (first iteration)

LM1021

When increasing the area of the elevators, the αtrim for each δe increases but the L/D ratio for those conditions decrease (expected behavior). Although the surface area of the elevators has been augmented almost 3 m2, the increase of alpha trim has not been significant; nose-up cruising can still be only achieved with an elevator deflection of -5 degrees with a reduction of the L/D ratio of 1.82% with respect to version 2. To be able to achieve nose-up cruising with lower elevator deflections, the elevator’s surface area would have to be increased. Nonetheless, this would reduce the generated lift hence diminish the lift over drag ratio. Also, bigger control surfaces imply bigger mechanical devices which are heavier. Therefore, it is decided to study version 2 of the LM1021 model assuming a deflection of -5 degrees while in cruise.

2 Elevator’s surface area [m ] δe αtrim L/Dtrim α(L/D)max L/Dmax dCL/dδe dCm/dδe LM1021 (v1) 6.3 0 -1.0697 12.603 0 13.572 1.2067e-3 -7.1050e-4 -1 -0.96938 12.48 0 13.426 -3 -0.76172 11.91 0.1904 12.884 -5 -0.55012 11.096 0.438 12.129 LM1021 (v2) 13.5 0 -1.0315 12.084 0 13.164 1.2067e-3 -7.1050e-4 -1 -0.81073 11.87 0.1543 12.856 -3 -0.3591 11.073 0.5272 11.899 -5 0.10807 10.09 0.921 10.71 LM1021 (v3) 16.22 0 -1.0066 11.973 0.0176 13.053 3.2300e-3 -1.7692e-3 -1 -0.74567 11.759 0.2019 12.707 -3 -0.20197 10.934 0.6227 11.64 -5 0.35539 9.9064 1.0594 10.344

Table 12.5: LM1021 elevator’s optimization

47 13 Dynamic Stability and Aircraft Perfor- mance

13.1 Theoretical Background

The dynamic stability deals with the motion of the aircraft. Apart from the aerodynamic forces already mentioned, two other forces need to be included in the analysis: the inertia forces and the damping forces. The aerodynamic damping forces resist motion and are dependent of the rotational speeds (p, q, r), as they vary as the effective α changes due to rotational motion. As for the mass moment of inertia, it describes the resistance of a body to rotational accelerations. A dynamically stable aircraft is such that, after being disturbed from an equilibrium condition, it goes back to its original condition immediately, or with some damped oscillations and overshooting. It is dynamically unstable if the oscillations caused by the disturbance are undamped, increasing their amplitude with time. If the amplitude is kept constant, the aircraft is said to have neutral dynamic stability. If the aircraft has any unstable behavior, the resulting oscillations need to be eliminated using passive or active methods. An aircraft can be represented in a state-space form which represents a small perturbation model for a set of nonlinear ODES x˙ = f(x, u):

x˙ = Ax + Bu (13.1) being • x ∈

→ • For an aircraft to be stable, the real part of the eigenvalues needs to be negative λ = λR±λI i, λR < 0 for stability

→ p 2 2 • Natural frequency: How fast the motion oscillates wn = λR + λI

→ • Damping ratio: How much amplitude decays per oscillation d=- λR wn • Period: Time that takes to complete one oscillation →τ = 2π wn • Half-life: Time that takes for amplitude to decay by half →γ = 0.693 |λR| 2. Forced response Assume x(0) = 0 and u = u(t) applied by pilot or control system → Particular solution/Zero state response 3. Complete response Sum of (1) and (2).

48 13.1.1 Longitudinal Dynamics The longitudinal dynamics are characterized by those movements that occur about the pitch axis (figure 13.1). In this case, the state and control vectors are the ones shown in below. There are two longitudinal dynamic modes (figure 13.2), the short-period mode and the long-period or phugoid mode.

 ∆u   ∆w  x =    ∆q  ∆Θ

 δ  u = T δe

Figure 13.1: Forces, moments, velocities and angles affected by the longitudinal motion of the aircraft.

Figure 13.2: Longitudinal modes represented in a Im-Re axis diagram.

The short period mode is a moderately damped mode that creates an oscillation of the nose about the velocity vector. The attitude, incidence and flight path angle of the aircraft change while the speed is kept constant. On the other hand, the phugoid mode is a lightly damped mode which consists in

49 an oscillatory exchange between the kinetic and potential energy of the system. When the aircraft does not have enough velocity, the nose falls down due to the lack of lift. As it falls down, it gains velocity, therefore lift, obtaining a nose-up attitude again. SDSA will be used to assess these modes using ESDU 92006 "A Background to the Handling Qualities of Aircraft" for the short period mode and ICAO recommendations for the phugoid mode.

13.1.2 Lateral dynamics The lateral dynamic of an aircraft is a combination of rolling, yawing and sideslip motions (figure 13.3). The controls and states involved in this type of movements are shown below. Three modes describe the lateral dynamics of an airplane: roll mode, spiral mode and dutch roll mode.

 ∆v   ∆p  x =    ∆r  ∆φ

 δ  u = a δr

Figure 13.3: Forces, moments, velocities and angles affected by the lateral motion.

The roll mode is a pure rotation about the x body axis; its primary force is the rolling moment. Rolling is used to keep the wings leveled in case of a disturbance and to change the heading angle. The spiral mode consists in a yaw motion at a non-zero bank angle coupled with a rolling motion. It is a very slow mode that can be either stable or unstable. Finally, the dutch roll mode is a damped oscillation in yaw that couples to roll. Its frequency is similar to the one of the short period mode but it is more lightly damped. For low-altitude flights, the problems caused due to the dutch roll are the yawing and how fast it can be damped. On the other hand, for high-speeds and high altitudes, the major concern is the rolling.

13.1.3 Handling Qualities An aircraft has to have acceptable flying qualities (also known as handling qualities) anywhere inside its operational flight envelope whether the engines are operating or not. It must have enough control power to maintain steady state, straight line flight and steady state maneuvering flight for mission objectives. It is required to have sufficient control power also to make transitions from ground operations to airborne operations and vice versa. Finally, the aircraft needs to be maneuverable from one steady state flight condition to another. In order to make sure that an aircraft has acceptable flying qualities, some regulations and scales need to be achieved. The Cooper-Harper pilot rating scale rates the flying qualities of a given airplane

50 in a given mission statement (figure 13.4). A pilot should not provide either too much or too little gain to the aircraft during any mission segment.

Figure 13.4: Cooper-Harper scale.

The MIL-F-8785C divides the aircrafts in different classes (figure 13.5), as each type of aircraft have different flying requirements. Each flight phase requires different types of pilot actions, therefore flying requirements also vary from one flight phase to another, making it necessary to create another list with different flight phases categories (figure 13.6). The flying qualities for each specific case (aircraft classification and flight phase) is rated using three different levels according to the MIL-F-8785C and MIL-STD-1797A regulations (figure 13.7).

13.2 Analysis of the SSBJs

Due to the limited amount of time, only two aerodynamic databases could be completed; the chosen models were the AS2 and the LM1021. From the three studied designs, only the Aerion AS2 has some probabilities to become a reality in the near future, therefore, finding out its flying behavior was a priority. The version used for this study is the original version (without resizing the elevator) as it was determined in section 12.3 as the better option. The HISAC model had already been investigated at KTH for the SimSAC project (for subsonic speeds and low altitudes) while nothing was known for the LM1021. The version 2 of the LM1021 was chosen as the second case of study for dynamic stability as it offered the best trimming characteristics.

51 Figure 13.5: Classification of aircrafts.

Figure 13.6: Classification of flight phases.

Figure 13.7: Flying quality levels.

52 13.2.1 AS2 As already mentioned in previous sections of this report, the primary focus of this study has been the longitudinal performance of the aircrafts (i.e. the phugoid and short-period modes). Figure 13.8 shows the results obtained with SDSA for heights between 14 km and 16 km and speeds of 430 m/s till 500 m/s, which correspond to cruising conditions. The short-period mode parameters are far from being satisfactory or even acceptable. The high natural frequencies make the aircraft too sensitive in maneuvering and too responsive to turbulence. The low period and damping ratios make it very excitable to control inputs and turbulence; also the resulting oscillations take longer to disappear. On the other hand, the phugoid mode parameters are in the satisfactory/acceptable region of the graph. The poor damping ratios make it more difficult to trim the vehicle, but the high periods allow more time to the pilot or the control loop to take control of this oscillation.

Figure 13.8: Longitudinal dynamic behavior of the Aerion AS2: short-period mode (top) and phugoid mode (bottom).

Trimming conditions and the static margin for cruise phase can be observed in figures 13.9 and 13.10 respectively. These results confirm the ones obtained while performing the static stability analysis (chapter 12). The AS2 is statically stable for all the points studied (positive static margin) and the angles of attack and elevator deflections are reasonable. The trimming angle of attack increases with the altitude but decreases with the speed. Although the behavior of the aircraft does not meet all the requirements and has to be improved, the initial results are not so catastrophic, as the aircraft is statically and dynamically stable at all times during the cruise regime. Further calculations should be done, this time taking into account aileron and rudder deflections, to study the lateral/directional flying qualities of the SSBJ.

13.2.2 LM1021 SDSA had some issues plotting the longitudinal modes and the trimming parameters for the Lockheed Martin model. This was due to the fact that the static margin obtained for low angles of attack was higher than 17% of the MAC (figure 13.11). To overcome this problem, the center of gravity of the LM1021

53 Figure 13.9: Angle of attack (top) and elevator deflection (bottom) needed to trim the AS2.

Figure 13.10: Static margin of the AS2 for different flying speeds and altitudes.

54 had to be moved 1.5 meters backwards towards the tail from its original position (the one calculated in chapter 10). This change does not pose a feasibility dilemma as the CG can be easily moved by slightly changing the position of the fuel tanks. The new static margin obtained with the CG translation can be seen in figure 13.12, the static margin has decreased but the aircraft remains statically stable for the whole studied region (positive static margin at all times).

Figure 13.11: Static margin of the LM1021 for different flying speeds and altitudes (original CG position).

Figure 13.12: Static margin of the LM1021 for changed CG location.

The longitudinal dynamic stability of this model has been studied for altitudes between 14000 and 16000 meters and speeds of 380 to 500 m/s (M = [1.3, 1.7]). The phugoid mode behavior is very similar to the one of the AS2(figure 13.13, bottom graph), in between the acceptable/satisfactory region. It is characterized by high periods and poor damping ratios, which make it difficult to trim the aircraft but still possible due to the amount of time the pilot or control system has to compensate the disturbance. Nonetheless, for some heights and speeds the phugoid mode becomes unstable (this cannot be seen on the graphs but is shown on the results given by SDSA). The real part of this mode becomes positive, hence unstable, for the following cases: 14500 m and M = [1.35, 1.39], 15000 m and M = [1.35, 1.42], 15500 m and M = [1.35, 1.49]; and 16000 m and M = [1.35, 1.66]. Bearing in mind that cruise conditions for the LM1021 are 1.6 M and 15240 m, this behavior is quite alarming. Although the aircraft is stable during cruise, if one of the parameters had to be changed for some reason, the jet could become unstable.

55 As for the short period mode (figure 13.13, top graph), the damping ratios are higher than for the AS2 but still unacceptable, avoiding quick self damping of the perturbations. The aircraft requires excessive compensation due to the low natural frequencies of the short period, which means trimming difficulties.

Figure 13.13: Longitudinal dynamic behavior of the LM1021: short period mode (top) and phugoid mode (bottom).

The trimming conditions can be observed in figure 13.14. The necessary angle of attack increases as the speed decreases and the altitude increases, just like with the AS2. Nonetheless, the values obtained are fairly higher than for the AS2 (around 7 degrees for the worst case scenario) which could affect greatly the L/D ratio of the aircraft. As for the elevator deflection required to trim the SSBJ, the values obtained are all in a reasonable range (no more than -6 degrees).

56 Figure 13.14: Trimming conditions for the LM1021: angle of attack (top), elevator deflection (bottom).

57 Part III

Conclusions

14 Main Goals

It has been possible to analyze the static stability of the SSBJs and optimize the size of the elevator surfaces meeting trimming requirements. All the studied aircrafts were statically stable for all weight conditions, except for the AS2 when operating under empty weight conditions. This, however, does not pose a problem as an airplane will never fly under this condition; there will always be some remnant of fuel and some payload such as crew members. Unexpectedly, the Aerion AS2 model had a reasonably good behavior with its initial elevator size. Nose-up cruise steady flight and high L/D ratio (> 9) was achieved even without elevator deflection. Its non-standard wing configuration for supersonic conditions (not delta-like wing) and the fact that the analyzed model was a very preliminary stage, made this finding very gratifying and surprising. Even though the HISAC and LM1021 configurations look more alike and could be at first glance comparable, the obtained results show that their behavior is very different when dealing with longitudinal static stability. With respect to the Lockheed Martin scaled down LM1021 version, the results found for the initial elevator surfaces were not satisfying as they implied nose-down cruising although with a very high L/D ratio (> 12), which is extremely important to have a better fuel economy. After increasing the size of the elevator, nose-up cruising was achieved with an elevator deflection of -5 degrees. This implied a diminishment of the L/D ratio but still considerably high (around 10). As for the HISAC model, the behavior obtained with the initial configuration was very poor regarding L/D trimming ratios; they were very far away from the maximum L/D ratios that could be accomplished. To try to overcome this issue, a canard was included. The results obtained with this modification were substantially better, achieving L/D trimming ratios as high as 7.9 for an elevator deflection of -5 degrees. Another of the main goals of the thesis, analyzing the early flying and handling qualities of the chosen supersonic business jets, has not been fully achieved. The lack of time made it impossible to complete the aerodynamic databases for the three chosen models. Nonetheless, there was time to assemble a reasonable database for the Aerion AS2, which is the model that has more probabilities to become a reality in a near future, and the Lockheed Martin LM1021. The results obtained for cruise phase show that more work has to be done concerning longitudinal dynamic stability, specially for the LM1021 model. The short-period mode behavior is unacceptable for both models, the AS2 has an excessive overshoot while the LM1021 requires excessive compensation. The phugoid mode for both aircrafts is in the limit between a satisfactory behavior for normal operation and an acceptable behavior for emergency condition, except for some flight conditions of the LM1021, where it becomes unstable (specified on section 13.2).

58 15 Learned Notions

During the six months of this research, many things have been learned regarding the process followed and the different programs that have been used. Learning how to use more than 10 different programs, that were completely unknown before starting this thesis, was not an easy task. Nevertheless, it was extremely useful as, besides from gaining a higher knowledge in CFD and completing the academic training, a methodology to learn how to use new software was acquired. To serve as an example of the learning curve, during the first months, a few weeks were necessary to obtain results from a new program but, by the end of the project, new software could be learned and results obtained in the same day. Also in relation to the amount and variety of programs used, it is worthy to mention the challenge of finding a way to adapt all the different outputs to be used as inputs for other programs. As already explained in the beginning, the process followed to complete this thesis has been an reverse design process. Three existing designs were chosen and analyzed to after modify some of their aspects to obtain a better behavior. This meant that having a good initial geometry with which to start the calculations was key to obtain accurate results. However, this was one of the most demanding and complicated aspects of the project, building models that would be simple enough to be able to obtain a mesh out of them but also reliable enough to obtain accurate results. Prior to the commencement of the thesis, the student had only elemental knowledge about Computa- tional Fluid Dynamics (CFD), her only experience being fumbling around with some codes whilst doing the major. After completing this project, a good understanding of how CFD software works has been acquired. Even though some emphasis has been put on the code itself and how the flow is solved, the learning process has been more focused on the user side: the importance of having a good geometry; getting a proper mesh fine enough to obtain accurate and trustworthy results; the importance of analyz- ing the obtained results and making sure they make sense and that convergence has been achieved; to mention a few specific examples.

16 Experience Using GoCart

GoCart has proven to be a very useful tool when wanting to solve the flow around a body for supersonic conditions. Its attractive interface and its easy use make it ideal for students who are being first intro- duced to the world of computational fluid dynamics. The available documentation and tutorials are very helpful when learning how to use the software. To be able to use all of GoCart’s capabilities (control deflection, mesh refinement, etc.) it is recom- mendable to build the geometry of the object that wants to be studied using Desktop Aeronautics’ CAD program RAGE. However, a few tricks have to be taken into account to obtain a functioning model for which a converged solution can be found. First of all, it is very important to position the control surfaces properly. If they are not well nudge, GoCart will have problems finding a converged solution, as weird shape elements will be formed trying to connect the different components. The best way to proceed is to slightly overlap the control surface and the surface it is being supported by (i.e. the aileron has to be barely touching the wing). To avoid problems with GoCart’s preprocessor and intersecting process, when defining the lifting surfaces (wing, tail, canard, etc.) in RAGE, only the y-coordinate of the wing apex should be set to 0. For the rest of wing-like surfaces, the apex’s y-coordinate should be different than zero, as if the “wings” were not joined at the center. Finally, the model introduced in GoCart has to be watertight to allow intersection of the components. This is easily achieved exporting the RAGE file (“.input”) to Cart3D format (“.tri”).

59 As for GoCart itself, there are some considerations the user should be aware of. When defining the desired mesh properties in the meshing section, the option of choosing y-symmetry is available. By se- lecting this alternative, the lateral/directional coefficients obtained are affected making them inaccurate. Moreover, to obtain good longitudinal coefficients, the reference area introduced in the flow solver section has to be half of the actual object’s area when specifying y-symmetry. There is no way to define the height at which the simulation should be run, therefore the changing properties of the atmosphere are not reflected on the results. GoCart implements NASA’s supersonic CFD code Cartd3D, so it is not surprising the fact that when trying to solve a subsonic case, the residuals obtained are very high or the solution does not even converge. Lastly, but not least, angular velocities cannot be implemented. This is a huge deficiency when trying to build an aerodynamic database for further studies. Nonetheless, GoCart does not cease to be a very good and helpful program. It offers quick and trustful results compared to other CFD codes such as Edge. What Edge takes around 1 hour and half to solve, GoCart does it in 20 minutes (77% faster). On the postprocessor section, the results are shown on the object that is being studied, making it easy to analyze the data visually. If the reference parameters that are used to normalize the aerodynamic coefficients change, there is no need to repeat the calculation, as the coefficients can be recalculated with just a click. But most importantly, α and Mach sweeps can be done automatically, one of the biggest benefits of GoCart’s solver. As it has been proved, GoCart is a very promising CFD software. A future collaboration between Desktop Aeronautics and KTH could be established to further develop GoCart while integrating it into CEASIOM. This would improve both programs and make them more complete.

17 Future Work

The most immediate work that would need to be done to improve this investigation is finding a way to build a complete and correct aerodynamic database to be able to carry out a full dynamic stability analysis. As already mentioned before, the fact that the existing aerodynamic databases have been built using two different programs, which calculate the aerodynamic coefficients in very different ways, is most probably not the best way to do it. The best approach would be building the database using only one software. The different options are the following: • Implement calculations with angular velocities in either Edge or GoCart. Edge would allow us calculating both subsonic and supersonic cases but the time taken would be very long plus α sweeps would have to be done manually. Also, a way to deflect the control surfaces would have to be thought. On the other hand, GoCart would go faster, sweeps would be done automatically and control deflection is done very easily building the model in RAGE but only the supersonic range could be studied. • Find another CFD code that is able to do subsonic and supersonic calculations with angular velocities and control deflections.

Regarding other aspects of the thesis, the following work could be done in a future:

• Improve the geometry of the supersonic business jets, specially the airfoils.

• Improve estimation of CG by defining the fuel deposits more accurately (was impossible to do due to the lack of information). As it has been proven in the dynamic stability analysis of the LM1021, the location of the center of gravity is essential to obtain a good/acceptable performance of the aircraft. %50 of a SSBJ’s weight is fuel, therefore, its CG is highly dependent on the position of the fuel tanks.

• Do further optimization loops for the elevator sizing.

60 • Improve CG estimations for HISAC model when adding a canard. • Study lateral/directional stability, therefore, rudder and aileron sizing. • Study other flight phases besides cruise.

61 Bibliography

[1] CEASIOM webpage, www.ceasiom.com [2] Tornado webpage, http://www.redhammer.se/tornado/ [3] GoCart’s training material webpage, https://wiki.desktop.aero:8443/pages/viewpage.action?pageId=7405775 [4] Aerion Corporation webpage, http://www.aerionsupersonic.com/

[5] D.P. Raymer, Aircraft Design: A Conceptual Approach. Fifth Edition, 2012. [6] M. Peet, Lecture 6: Neutral Point and Elevator Control. Notes from the Spacecraft and Aircraft Dynamics course at Illinois Institute of Technology. http://control.asu.edu/Classes/MMAE441/Aircraft/441Lecture6.pdf

[7] T. Goetzendorf-Grabowski,D. Mieszalski, E. Marcinkiewicz, Stability analysis using SDSA tool. Progress in Aerospace Sciences, 47, pg 636-646, 2011. [8] M. Drela, A User’s Guide to MSES 3.05. MIT Department of Aeronautics and Astronautics, USA, 2011.

[9] N. Ceresola, Enhanced Tier-I Design for Existing Configuration. SimSAC delivery report 6.3-3. Alenia Aeronautica, Dassault Aviation, DLR, 2010. [10] R.K. Nangia, M.E. Palmer, R.H. Doe, Towards Design of Mach 1.6+ Cruise Aircraft. 22nd AIAA Applied Aerodynamics Meeting Exhibit (AIAA 2004-5070), Providence, Rhode Island, USA, 2004. [11] B.F. Niehaus, The USAF Stability and Control Digital DATCOM. Volume I, Users Manual. Mc- Donell Douglas Astronautics Company - St. Louis Division, St. Louis, Missouri, USA, 1979. [12] P. Sturdza, An Aerodynamic Design Method for Supersonic Natural Laminar Flow Aircraft. Disser- tation for PhD, Standford University, USA, 2003. [13] P.A. Henne, Case for Small Supersonic Civil Aircraft. Journal of Aircraft, Vol. 42, No. 3, USA, 2005. [14] I. Poll, The Prospects and Issues for Supersonic Business Jets. Crafield University, UK.

[15] K. Sakata, Japan’s Supersonic Technology and Business Jet Perspectives. 51st AIAA Aerospace Sciences Meeting (AIAA 2013-0021), Grapevone, Texas, USA, 2013.

[16] S. Choi, J.J. Alonso, I.M. Kroo, M. Wintzer Multifidelity Design Optimization Low-Boom Supersonic Jets. Journal of Aircraft, Vol. 45, No. 1, USA, 2008. [17] Isikveren, A.T. Quasi-Analytical Modelling and Optimisation Techniques for Transport Aircraft De- sign. Doctoral Thesis Report, Montreal, Quebec, Canada, 2002-2013. [18] P. Sturdza, Extensive Supersonic Natural Laminar Flow on the Aerion Business Jet. 45th AIAA Aerospace Sciences Meeting and Exhibition, Reno, Nevada, USA, 2007. [19] H.R. Welge, C. Nelson, J. Bonet, Supersonic Vehicle Systems for the 2020 to 2035 Timeframe. 28th AIAA Applied Aerodynamics Conference (AIAA 2010-4930), Chicago, Illinois, USA, 2010. [20] R.K. Nangia, M.E. Palmer, K.P. Iwanski, Towards Design of Long-Range Supersonic Military Air- craft. 22th AIAA Applied Aerodynamics Conference and Exhibit (AIAA 2004-5071), Providence, Rhode Island, USA, 2004.

62 [21] R.K. Nangia, M.E. Palmer, R.H. Doe, A Study of Supersonic Aircraft With Thin Wings of Low Sweep. 40th AIAA Aerospace Sciences Meeting and Exhibit (AIAA 2002-0709), Reno, Nevada, USA, 2002. [22] J. Morgenstern, N. Norstrud, J. Sokhey, S. Martens, J.J. Alonso Advanced Concept Studies for Su- personic Commercial Transports Entering Service in the 2018 to 2020 Period. Phase I Final Report.. Lockheed Martin Corporation, NASA/CR 2013-217820 Palmdale, California, USA, 2013. [23] J. Morgenstern, M. Buonanno, F. Marconi, Full Configuration Low Boom Model and Grids for 2014 Sonic Boom Prediction Workshop. 51st AIAA Aerospace Sciences Meeting (AIAA 2013-0647), Grapevine, Texas, USA, 2013.

[24] J. Morgenstern, M. Buonanno, S. Chai, F. Marconi, Overview of Sonic Boom Reduction Efforts on the Lockheed Martin N+2 Supersonic Validations Program. 32nd AIAA Applied Aerodynamics Conference (AIAA 2014-2138), Atltanta, Georgia, USA, 2014. [25] J.J. Dickeson, A.A. Rodriguez, S. Sridharan, A. Korad, Elevator Sizing, Placement, and Control- Relevant Tradeoffs for Hypersonic Vehicles. AIAA Guidance, Navigation and Control Conference (AIAA 2010-8339), Toronto, Ontario, Canada, 2013. [26] ESDU 76003 Geometrical properties of cranked and straight-tapered wing planforms. 2012.

63 Appendix: Database with "Existing" Super- sonic Business Jets

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